Matching Items (634)
Filtering by
- Creators: School of Mathematical and Statistical Sciences
- Member of: Theses and Dissertations
Description
Reductive dechlorination by members of the bacterial genus Dehalococcoides is a common and cost-effective avenue for in situ bioremediation of sites contaminated with the chlorinated solvents, trichloroethene (TCE) and perchloroethene (PCE). The overarching goal of my research was to address some of the challenges associated with bioremediation timeframes by improving the rates of reductive dechlorination and the growth of Dehalococcoides in mixed communities. Biostimulation of contaminated sites or microcosms with electron donor fails to consistently promote dechlorination of PCE/TCE beyond cis-dichloroethene (cis-DCE), even when the presence of Dehalococcoides is confirmed. Supported by data from microcosm experiments, I showed that the stalling at cis-DCE is due a H2 competition in which components of the soil or sediment serve as electron acceptors for competing microorganisms. However, once competition was minimized by providing selective enrichment techniques, I illustrated how to obtain both fast rates and high-density Dehalococcoides using three distinct enrichment cultures. Having achieved a heightened awareness of the fierce competition for electron donor, I then identified bicarbonate (HCO3-) as a potential H2 sink for reductive dechlorination. HCO3- is the natural buffer in groundwater but also the electron acceptor for hydrogenotrophic methanogens and homoacetogens, two microbial groups commonly encountered with Dehalococcoides. By testing a range of concentrations in batch experiments, I showed that methanogens are favored at low HCO3 and homoacetogens at high HCO3-. The high HCO3- concentrations increased the H2 demand which negatively affected the rates and extent of dechlorination. By applying the gained knowledge on microbial community management, I ran the first successful continuous stirred-tank reactor (CSTR) at a 3-d hydraulic retention time for cultivation of dechlorinating cultures. I demonstrated that using carefully selected conditions in a CSTR, cultivation of Dehalococcoides at short retention times is feasible, resulting in robust cultures capable of fast dechlorination. Lastly, I provide a systematic insight into the effect of high ammonia on communities involved in dechlorination of chloroethenes. This work documents the potential use of landfill leachate as a substrate for dechlorination and an increased tolerance of Dehalococcoides to high ammonia concentrations (2 g L-1 NH4+-N) without loss of the ability to dechlorinate TCE to ethene.
ContributorsDelgado, Anca Georgiana (Author) / Krajmalnik-Brown, Rosa (Thesis advisor) / Cadillo-Quiroz, Hinsby (Committee member) / Halden, Rolf U. (Committee member) / Rittmann, Bruce E. (Committee member) / Stout, Valerie (Committee member) / Arizona State University (Publisher)
Created2013
Description
In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$-eigenspace component of the $p$-Sylow subgroup of the class group of the field at the $m$-th level in a $\mathbb{Z}_p$-extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}-1,f(T,\omega^{1-i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us with a powerful connection between algebraic and analytic techniques; however, as of yet, this isomorphism is unestablished in general. I consider the existence and the properties of an exact sequence $$0\longrightarrow\ker{\longrightarrow}CG_m^i{\longrightarrow}IACG_m^i{\longrightarrow}\textrm{coker}\longrightarrow0.$$ In the case of a $\mathbb{Z}_p$-extension where the Main Conjecture is established, there exists a pseudo-isomorphism between the respective inverse limits of $CG_m^i$ and $IACG_m^i$. I consider conditions for when such a pseudo-isomorphism immediately gives the existence of the desired exact sequence, and I also consider work-around methods that preserve cardinality for otherwise. However, I primarily focus on constructing conditions to verify if a given $m$ is sufficiently large that the kernel and cokernel of the above exact sequence have become well-behaved, providing similarity of growth both in the size and in the structure of $CG_m^i$ and $IACG_m^i$; as well as conditions to determine if any such $m$ exists. The primary motivating idea is that if $IACG_m^i$ is relatively easy to work with, and if the relationship between $CG_m^i$ and $IACG_m^i$ is understood; then $CG_m^i$ becomes easier to work with. Moreover, while the motivating framework is stated concretely in terms of the cyclotomic $\mathbb{Z}_p$-extension of $p$-power roots of unity, all results are generally applicable to arbitrary $\mathbb{Z}_p$-extensions as they are developed in terms of Iwasawa-Theory-inspired, yet abstracted, algebraic results on maps between inverse limits.
ContributorsElledge, Shawn Michael (Author) / Childress, Nancy (Thesis advisor) / Bremner, Andrew (Committee member) / Fishel, Susanna (Committee member) / Jones, John (Committee member) / Paupert, Julien (Committee member) / Arizona State University (Publisher)
Created2013
Description
In 1984, Sinnott used $p$-adic measures on $\mathbb{Z}_p$ to give a new proof of the Ferrero-Washington Theorem for abelian number fields by realizing $p$-adic $L$-functions as (essentially) the $Gamma$-transform of certain $p$-adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$-adic $L$-functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$-adic $L$-functions as $Gamma$-transforms of certain $p$-adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$-invariant for certain $mathbb{Z}_p$-extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves.
In this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
In this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
ContributorsZinzer, Scott Michael (Author) / Childress, Nancy (Thesis advisor) / Bremner, Andrew (Committee member) / Fishel, Susanna (Committee member) / Jones, John (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2015
Description
Despite the breadth of studies investigating ecosystem development, an underlying theory guiding this process remains elusive. Several principles have been proposed to explain ecosystem development, though few have garnered broad support in the literature. I used boreal wetland soils as a study system to test a notable goal oriented principle: The Maximum Power Principle (MPP). The MPP posits that ecosystems, and in fact all energy systems, develop to maximize power production or the rate of energy production. I conducted theoretical and empirical investigations to test the MPP in northern wetlands.
Permafrost degradation is leading to rapid wetland formation in northern peatland ecosystems, altering the role of these ecosystems in the global carbon cycle. I reviewed the literature on the history of the MPP theory, including tracing its origins to The Second Law of Thermodynamics. To empirically test the MPP, I collected soils along a gradient of ecosystem development and: 1) quantified the rate of adenosine triphosphate (ATP) production--literally cellular energy--to test the MPP; 2) quantified greenhouse gas production (CO2, CH4, and N2O) and microbial genes that produce enzymes catalyzing greenhouse gas production, and; 3) sequenced the 16s rRNA gene from soil microbes to investigate microbial community composition across the chronosequence of wetland development. My results suggested that the MPP and other related theoretical constructs have strong potential to further inform our understanding of ecosystem development. Soil system power (ATP) decreased temporarily as the ecosystem reorganized after disturbance to rates of power production that approached pre-disturbance levels. Rates of CH4 and N2O production were higher at the newly formed bog and microbial genes involved with greenhouse gas production were strongly related to the amount of greenhouse gas produced. DNA sequencing results showed that across the chronosequence of development, the two relatively mature ecosystems--the peatland forest ecosystem prior to permafrost degradation and the oldest bog--were more similar to one another than to the intermediate, less mature bog. Collectively, my results suggest that ecosystem age, rather than ecosystem state, was a more important driver for ecosystem structure and function.
Permafrost degradation is leading to rapid wetland formation in northern peatland ecosystems, altering the role of these ecosystems in the global carbon cycle. I reviewed the literature on the history of the MPP theory, including tracing its origins to The Second Law of Thermodynamics. To empirically test the MPP, I collected soils along a gradient of ecosystem development and: 1) quantified the rate of adenosine triphosphate (ATP) production--literally cellular energy--to test the MPP; 2) quantified greenhouse gas production (CO2, CH4, and N2O) and microbial genes that produce enzymes catalyzing greenhouse gas production, and; 3) sequenced the 16s rRNA gene from soil microbes to investigate microbial community composition across the chronosequence of wetland development. My results suggested that the MPP and other related theoretical constructs have strong potential to further inform our understanding of ecosystem development. Soil system power (ATP) decreased temporarily as the ecosystem reorganized after disturbance to rates of power production that approached pre-disturbance levels. Rates of CH4 and N2O production were higher at the newly formed bog and microbial genes involved with greenhouse gas production were strongly related to the amount of greenhouse gas produced. DNA sequencing results showed that across the chronosequence of development, the two relatively mature ecosystems--the peatland forest ecosystem prior to permafrost degradation and the oldest bog--were more similar to one another than to the intermediate, less mature bog. Collectively, my results suggest that ecosystem age, rather than ecosystem state, was a more important driver for ecosystem structure and function.
ContributorsChapman, Eric (Author) / Childers, Daniel L. (Thesis advisor) / Cadillo-Quiroz, Hinsby (Committee member) / Hall, Sharon J (Committee member) / Turetsky, Merritt (Committee member) / Arizona State University (Publisher)
Created2015
Description
Peatlands represent 3% of the earth’s surface but have been estimated to contain up to 30% of all terrestrial soil organic carbon and release an estimated 40% of global atmospheric CH4 emissions. Contributors to the production of CH4 are methanogenic Archaea through a coupled metabolic dependency of end products released by heterotrophic bacteria within the soil in the absence of O2. To better understand how neighboring bacterial communities can influence methanogenesis, the isolation and physiological characterization of two novel isolates, one Methanoarchaeal isolate and one Acidobacterium isolate identified as QU12MR and R28S, respectively, were targeted in this present study. Co-culture growth in varying temperatures of the QU12MR isolate paired with an isolated Clostridium species labeled R32Q and the R28S isolate were also investigated for possible influences in CH4 production. Phylogenetic analysis of strain QU12MR was observed as a member of genus Methanobacterium sharing 98% identity similar to M. arcticum strain M2 and 99% identity similar to M. uliginosum strain P2St. Phylogenetic analysis of strain R28S was associated with genus Acidicapsa from the phylum Acidobacteria, sharing 97% identity to A. acidisoli strain SK-11 and 96% identity similarity to Occallatibacter savannae strain A2-1c. Bacterial co-culture growth and archaeal CH4 production was present in the five temperature ranges tested. However, bacterial growth and archaeal CH4 production was less than what was observed in pure culture analysis after 21 days of incubation.
ContributorsRamirez, Zeni Elizia (Author) / Cadillo-Quiroz, Hinsby (Thesis advisor) / Roberson, Robert (Thesis advisor) / Wang, Xuan (Committee member) / Arizona State University (Publisher)
Created2018
Description
In the 1980's, Gromov and Piatetski-Shapiro introduced a technique called "hybridization'' which allowed them to produce non-arithmetic hyperbolic lattices from two non-commensurable arithmetic lattices. It has been asked whether an analogous hybridization technique exists for complex hyperbolic lattices, because certain geometric obstructions make it unclear how to adapt this technique. This thesis explores one possible construction (originally due to Hunt) in depth and uses it to produce arithmetic lattices, non-arithmetic lattices, and thin subgroups in SU(2,1).
ContributorsWells, Joseph (Author) / Paupert, Julien (Thesis advisor) / Kotschwar, Brett (Committee member) / Childress, Nancy (Committee member) / Fishel, Susanna (Committee member) / Kawski, Matthias (Committee member) / Arizona State University (Publisher)
Created2019
Description
Diophantine arithmetic is one of the oldest branches of mathematics, the search
for integer or rational solutions of algebraic equations. Pythagorean triangles are
an early instance. Diophantus of Alexandria wrote the first related treatise in the
fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat.
The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application to Diophantine equations. This theory is used in application to the problems studied in this thesis. This thesis studies some curves of high genus, and possible solutions in both rationals and in algebraic number fields, generalizes some old results and gives answers to some open problems in the literature. The methods involve known techniques together with some ingenious tricks. For example, the equations $y^2=x^6+k$, $k=-39,\,-47$, the two previously unsolved cases for $|k|<50$, are solved using algebraic number theory and the ‘elliptic Chabauty’ method. The thesis also studies the genus three quartic curves $F(x^2,y^2,z^2)=0$ where F is a homogeneous quadratic form, and extend old results of Cassels, and Bremner. It is a very delicate matter to find such curves that have no rational points, yet which do have points in odd-degree extension fields of the rationals.
The principal results of the thesis are related to surfaces where the theory is much less well known. In particular, the thesis studies some specific families of surfaces, and give a negative answer to a question in the literature regarding representation of integers n in the form $n=(x+y+z+w)(1/x+1/y+1/z+1/w).$ Further, an example, the first such known, of a quartic surface $x^4+7y^4=14z^4+18w^4$ is given with remarkable properties: it is everywhere locally solvable, yet has no non-zero rational point, despite having a point in (non-trivial) odd-degree extension fields of the rationals. The ideas here involve manipulation of the Hilbert symbol, together with the theory of elliptic curves.
for integer or rational solutions of algebraic equations. Pythagorean triangles are
an early instance. Diophantus of Alexandria wrote the first related treatise in the
fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat.
The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application to Diophantine equations. This theory is used in application to the problems studied in this thesis. This thesis studies some curves of high genus, and possible solutions in both rationals and in algebraic number fields, generalizes some old results and gives answers to some open problems in the literature. The methods involve known techniques together with some ingenious tricks. For example, the equations $y^2=x^6+k$, $k=-39,\,-47$, the two previously unsolved cases for $|k|<50$, are solved using algebraic number theory and the ‘elliptic Chabauty’ method. The thesis also studies the genus three quartic curves $F(x^2,y^2,z^2)=0$ where F is a homogeneous quadratic form, and extend old results of Cassels, and Bremner. It is a very delicate matter to find such curves that have no rational points, yet which do have points in odd-degree extension fields of the rationals.
The principal results of the thesis are related to surfaces where the theory is much less well known. In particular, the thesis studies some specific families of surfaces, and give a negative answer to a question in the literature regarding representation of integers n in the form $n=(x+y+z+w)(1/x+1/y+1/z+1/w).$ Further, an example, the first such known, of a quartic surface $x^4+7y^4=14z^4+18w^4$ is given with remarkable properties: it is everywhere locally solvable, yet has no non-zero rational point, despite having a point in (non-trivial) odd-degree extension fields of the rationals. The ideas here involve manipulation of the Hilbert symbol, together with the theory of elliptic curves.
ContributorsNguyen, Xuan Tho (Author) / Bremner, Andrew (Thesis advisor) / Childress, Nancy (Committee member) / Jones, John (Committee member) / Quigg, John (Committee member) / Fishel, Susanna (Committee member) / Arizona State University (Publisher)
Created2019
Description
Utilizing both 16S and 18S rRNA sequencing alongside energetic calculations from geochemical measurements offers a bridged perspective of prokaryotic and eukaryotic community diversities and their relationships to geochemical diversity. Yellowstone National Park hot spring outflows from varied geochemical compositions, ranging in pH from < 2 to > 9 and in temperature from < 30°C to > 90°C, were sampled across the photosynthetic fringe, a transition in these outflows from exclusively chemosynthetic microbial communities to those that include photosynthesis. Illumina sequencing was performed to document the diversity of both prokaryotes and eukaryotes above, at, and below the photosynthetic fringe of twelve hot spring systems. Additionally, field measurements of dissolved oxygen, ferrous iron, and total sulfide were combined with laboratory analyses of sulfate, nitrate, total ammonium, dissolved inorganic carbon, dissolved methane, dissolved hydrogen, and dissolved carbon monoxide were used to calculate the available energy from 58 potential metabolisms. Results were ranked to identify those that yield the most energy according to the geochemical conditions of each system. Of the 46 samples taken across twelve systems, all showed the greatest energy yields using oxygen as the main electron acceptor, followed by nitrate. On the other hand, ammonium or ammonia, depending on pH, showed the greatest energy yields as an electron donor, followed by H2S or HS-. While some sequenced taxa reflect potential biotic participants in the sulfur cycle of these hot spring systems, many sample locations that yield the most energy from ammonium/ammonia oxidation have low relative abundances of known ammonium/ammonia oxidizers, indicating potentially untapped sources of chemotrophic energy or perhaps poorly understood metabolic capabilities of cultured chemotrophs.
ContributorsRomero, Joseph Thomas (Author) / Shock, Everett L (Thesis advisor) / Cadillo-Quiroz, Hinsby (Committee member) / Till, Christy B. (Committee member) / Arizona State University (Publisher)
Created2018
Description
This research compares shifts in a SuperSpec titanium nitride (TiN) kinetic inductance detector's (KID's) resonant frequency with accepted models for other KIDs. SuperSpec, which is being developed at the University of Colorado Boulder, is an on-chip spectrometer designed with a multiplexed readout with multiple KIDs that is set up for a broadband transmission of these measurements. It is useful for detecting radiation in the mm and sub mm wavelengths which is significant since absorption and reemission of photons by dust causes radiation from distant objects to reach us in infrared and far-infrared bands. In preparation for testing, our team installed stages designed previously by Paul Abers and his group into our cryostat and designed and installed other parts necessary for the cryostat to be able to test devices on the 250 mK stage. This work included the design and construction of additional parts, a new setup for the wiring in the cryostat, the assembly, testing, and installation of several stainless steel coaxial cables for the measurements through the devices, and other cryogenic and low pressure considerations. The SuperSpec KID was successfully tested on this 250 mK stage thus confirming that the new setup is functional. Our results are in agreement with existing models which suggest that the breaking of cooper pairs in the detector's superconductor which occurs in response to temperature, optical load, and readout power will decrease the resonant frequencies. A negative linear relationship in our results appears, as expected, since the parameters are varied only slightly so that a linear approximation is appropriate. We compared the rate at which the resonant frequency responded to temperature and found it to be close to the expected value.
ContributorsDiaz, Heriberto Chacon (Author) / Mauskopf, Philip (Thesis director) / McCartney, Martha (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This paper considers what factors influence student interest, motivation, and continued engagement. Studies show anticipated extrinsic rewards for activity participation have been shown to reduce intrinsic value for that activity. This might suggest that grade point average (GPA) has a similar effect on academic interests. Further, when incentives such as scholarships, internships, and careers are GPA-oriented, students must adopt performance goals in courses to guarantee success. However, performance goals have not been shown to correlated with continued interest in a topic. Current literature proposes that student involvement in extracurricular activities, focused study groups, and mentored research are crucial to student success. Further, students may express either a fixed or growth mindset, which influences their approach to challenges and opportunities for growth. The purpose of this study was to collect individual cases of students' experiences in college. The interview method was chosen to collect complex information that could not be gathered from standard surveys. To accomplish this, questions were developed based on content areas related to education and motivation theory. The content areas included activities and meaning, motivation, vision, and personal development. The developed interview method relied on broad questions that would be followed by specific "probing" questions. We hypothesize that this would result in participant-led discussions and unique narratives from the participant. Initial findings suggest that some of the questions were effective in eliciting detailed responses, though results were dependent on the interviewer. From the interviews we find that students value their group involvements, leadership opportunities, and relationships with mentors, which parallels results found in other studies.
ContributorsAbrams, Sara (Author) / Hartwell, Lee (Thesis director) / Correa, Kevin (Committee member) / Department of Psychology (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05