Hadamard Well-Posedness for two Nonlinear Structure Acoustic Models

This dissertation focuses on the Hadamard well-posedness of two nonlinear structure acoustic models, each consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ strongly coupled with a Berger plate equation acting only on a flat portion of the boundary of $\Omega$. In each case, the PDE is of the following form: \begin{align*} \begin{cases} u_{tt}-\Delta u +g_1(u_t)=f(u) &\text{ in } \Omega \times (0,T),\\[1mm] w_{tt}+\Delta^2w+g_2(w_t)+u_t|_{\Gamma}=h(w)&\text{ in }\Gamma\times(0,T),\\[1mm] u=0&\text{ on }\Gamma_0\times(0,T),\\[1mm] \partial_\nu u=w_t&\text{ on }\Gamma\times(0,T),\\[1mm] w=\partial_{\nu_\Gamma}w=0&\text{ on }\partial\Gamma\times(0,T),\\[1mm] (u(0),u_t(0))=(u_0,u_1),\hspace{5mm}(w(0),w_t(0))=(w_0,w_1), \end{cases} \end{align*} where the initial data reside in the finite energy space, i.e., $$(u_0, u_1)\in H^1_{\Gamma_0}(\Omega) \times L^2(\Omega) \, \text{ and }(w_0, w_1)\in H^2_0(\Gamma)\times L^2(\Gamma).$$ The chief assumption of the first model is in taking $f(u)=-u|u|^{p-1}$, i.e., $f$ is a restoring source, where $p\geq 1$ is arbitrary. A standard Galerkin approximation scheme is used to establish a rigorous proof of the existence of local weak solutions. In addition, under some conditions on the parameters in the system, it is shown that such solutions exist globally in time and depend continuously on the initial data. For the second model, $f$ is taken to be an energy building source, and in particular it is allowed to have a \emph{supercritical} exponent, in the sense that its associated Nemytskii operators is not locally Lipschitz from $H^1_{\Gamma_0}(\Omega)$ into $L^2(\Omega)$. By employing nonlinear semigroups and the theory of monotone operators, several results on the existence of local and global weak solutions are obtained. Moreover, it is proven that such solutions depend continuously on the initial data, and uniqueness is obtained in two different scenarios. Adviser: Mohammad A. Rammah

Transiting Disintegrating Planetary Debris around WD 1145+017

More than a decade after astronomers realized that disrupted planetary material likely pollutes the surfaces of many white dwarf stars, the discovery of transiting debris orbiting the white dwarf WD 1145+017 has opened the door to new explorations of this process. We describe the observational evidence for transiting planetary material and the current theoretical understanding (and in some cases lack thereof) of the phenomenon.Comment: Invited review chapter. Accepted March 23, 2017 and published October 7, 2017 in the Handbook of Exoplanets. 15 pages, 10 figure

Huntingtin Interacting Proteins Are Genetic Modifiers of Neurodegeneration

Huntington's disease (HD) is a fatal neurodegenerative condition caused by expansion of the polyglutamine tract in the huntingtin (Htt) protein. Neuronal toxicity in HD is thought to be, at least in part, a consequence of protein interactions involving mutant Htt. We therefore hypothesized that genetic modifiers of HD neurodegeneration should be enriched among Htt protein interactors. To test this idea, we identified a comprehensive set of Htt interactors using two complementary approaches: high-throughput yeast two-hybrid screening and affinity pull down followed by mass spectrometry. This effort led to the identification of 234 high-confidence Htt-associated proteins, 104 of which were found with the yeast method and 130 with the pull downs. We then tested an arbitrary set of 60 genes encoding interacting proteins for their ability to behave as genetic modifiers of neurodegeneration in a Drosophila model of HD. This high-content validation assay showed that 27 of 60 orthologs tested were high-confidence genetic modifiers, as modification was observed with more than one allele. The 45% hit rate for genetic modifiers seen among the interactors is an order of magnitude higher than the 1%–4% typically observed in unbiased genetic screens. Genetic modifiers were similarly represented among proteins discovered using yeast two-hybrid and pull-down/mass spectrometry methods, supporting the notion that these complementary technologies are equally useful in identifying biologically relevant proteins. Interacting proteins confirmed as modifiers of the neurodegeneration phenotype represent a diverse array of biological functions, including synaptic transmission, cytoskeletal organization, signal transduction, and transcription. Among the modifiers were 17 loss-of-function suppressors of neurodegeneration, which can be considered potential targets for therapeutic intervention. Finally, we show that seven interacting proteins from among 11 tested were able to co-immunoprecipitate with full-length Htt from mouse brain. These studies demonstrate that high-throughput screening for protein interactions combined with genetic validation in a model organism is a powerful approach for identifying novel candidate modifiers of polyglutamine toxicity

A dynamic leaf gas-exchange strategy is conserved in woody plants under changing ambient CO2: evidence from carbon isotope discrimination in paleo and CO2 enrichment studies

Rising atmospheric [CO2 ], ca , is expected to affect stomatal regulation of leaf gas-exchange of woody plants, thus influencing energy fluxes as well as carbon (C), water and nutrient cycling of forests. Researchers have proposed various strategies for stomatal regulation of leaf gas-exchange that include maintaining a constant leaf internal [CO2 ], ci , a constant drawdown in CO2 (ca - ci ), and a constant ci /ca . These strategies can result in drastically different consequences for leaf gas-exchange. The accuracy of Earth systems models depends in part on assumptions about generalizable patterns in leaf gas-exchange responses to varying ca . The concept of optimal stomatal behavior, exemplified by woody plants shifting along a continuum of these strategies, provides a unifying framework for understanding leaf gas-exchange responses to ca . To assess leaf gas-exchange regulation strategies, we analyzed patterns in ci inferred from studies reporting C stable isotope ratios (δ(13) C) or photosynthetic discrimination (∆) in woody angiosperms and gymnosperms that grew across a range of ca spanning at least 100 ppm. Our results suggest that much of the ca -induced changes in ci /ca occurred across ca spanning 200 to 400 ppm. These patterns imply that ca - ci will eventually approach a constant level at high ca because assimilation rates will reach a maximum and stomatal conductance of each species should be constrained to some minimum level. These analyses are not consistent with canalization towards any single strategy, particularly maintaining a constant ci . Rather, the results are consistent with the existence of a broadly conserved pattern of stomatal optimization in woody angiosperms and gymnosperms. This results in trees being profligate water users at low ca , when additional water loss is small for each unit of C gain, and increasingly water-conservative at high ca , when photosystems are saturated and water loss is large for each unit C gain. This article is protected by copyright. All rights reserved.Rising atmospheric [CO2], c(a), is expected to affect stomatal regulation of leaf gas-exchange of woody plants, thus influencing energy fluxes as well as carbon (C), water, and nutrient cycling of forests. Researchers have proposed various strategies for stomatal regulation of leaf gas-exchange that include maintaining a constant leaf internal [CO2], c(i), a constant drawdown in CO2 (c(a)-c(i)), and a constant c(i)/c(a). These strategies can result in drastically different consequences for leaf gas-exchange. The accuracy of Earth systems models depends in part on assumptions about generalizable patterns in leaf gas-exchange responses to varying c(a). The concept of optimal stomatal behavior, exemplified by woody plants shifting along a continuum of these strategies, provides a unifying framework for understanding leaf gas-exchange responses to c(a). To assess leaf gas-exchange regulation strategies, we analyzed patterns in c(i) inferred from studies reporting C stable isotope ratios (C-13) or photosynthetic discrimination () in woody angiosperms and gymnosperms that grew across a range of c(a) spanning at least 100ppm. Our results suggest that much of the c(a)-induced changes in c(i)/c(a) occurred across c(a) spanning 200 to 400ppm. These patterns imply that c(a)-c(i) will eventually approach a constant level at high c(a) because assimilation rates will reach a maximum and stomatal conductance of each species should be constrained to some minimum level. These analyses are not consistent with canalization toward any single strategy, particularly maintaining a constant c(i). Rather, the results are consistent with the existence of a broadly conserved pattern of stomatal optimization in woody angiosperms and gymnosperms. This results in trees being profligate water users at low c(a), when additional water loss is small for each unit of C gain, and increasingly water-conservative at high c(a), when photosystems are saturated and water loss is large for each unit C gain

Capabilities, Performance, and Status of the SOFIA Science Instrument Suite

The Stratospheric Observatory for Infrared Astronomy (SOFIA) is an airborne observatory, carrying a 2.5 m telescope onboard a heavily modified Boeing 747SP aircraft. SOFIA is optimized for operation at infrared wavelengths, much of which is obscured for ground-based observatories by atmospheric water vapor. The SOFIA science instrument complement consists of seven instruments: FORCAST (Faint Object InfraRed CAmera for the SOFIA Telescope), GREAT (German Receiver for Astronomy at Terahertz Frequencies), HIPO (High-speed Imaging Photometer for Occultations), FLITECAM (First Light Infrared Test Experiment CAMera), FIFI-LS (Far-Infrared Field-Imaging Line Spectrometer), EXES (Echelon-Cross-Echelle Spectrograph), and HAWC (High-resolution Airborne Wideband Camera). FORCAST is a 540 m imager with grism spectroscopy, developed at Cornell University. GREAT is a heterodyne spectrometer providing high-resolution spectroscopy in several bands from 60240 m, developed at the Max Planck Institute for Radio Astronomy. HIPO is a 0.31.1 m imager, developed at Lowell Observatory. FLITECAM is a 15 m wide-field imager with grism spectroscopy, developed at UCLA. FIFI-LS is a 42210 m integral field imaging grating spectrometer, developed at the University of Stuttgart. EXES is a 528 m high-resolution spectrograph, developed at UC Davis and NASA ARC. HAWC is a 50240 m imager, developed at the University of Chicago, and undergoing an upgrade at JPL to add polarimetry capability and substantially larger GSFC detectors. We describe the capabilities, performance, and status of each instrument, highlighting science results obtained using FORCAST, GREAT, and HIPO during SOFIA Early Science observations conducted in 2011

The Space Infrared Interferometric Telescope (SPIRIT): High-resolution imaging and spectroscopy in the far-infrared

We report results of a recently-completed pre-Formulation Phase study of SPIRIT, a candidate NASA Origins Probe mission. SPIRIT is a spatial and spectral interferometer with an operating wavelength range 25 - 400 microns. SPIRIT will provide sub-arcsecond resolution images and spectra with resolution R = 3000 in a 1 arcmin field of view to accomplish three primary scientific objectives: (1) Learn how planetary systems form from protostellar disks, and how they acquire their inhomogeneous composition; (2) characterize the family of extrasolar planetary systems by imaging the structure in debris disks to understand how and where planets of different types form; and (3) learn how high-redshift galaxies formed and merged to form the present-day population of galaxies. Observations with SPIRIT will be complementary to those of the James Webb Space Telescope and the ground-based Atacama Large Millimeter Array. All three observatories could be operational contemporaneously.Comment: 20 pages, 12 figures, accepted for publication in J. Adv. Space Res. on 26 May 200

Hadamard Well-Posedness for two Nonlinear Structure Acoustic Models

This dissertation focuses on the Hadamard well-posedness of two nonlinear structure acoustic models, each consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ strongly coupled with a Berger plate equation acting only on a flat portion of the boundary of $\Omega$. In each case, the PDE is of the following form: \begin{align*} \begin{cases} u_{tt}-\Delta u +g_1(u_t)=f(u) &\text{ in } \Omega \times (0,T),\\[1mm] w_{tt}+\Delta^2w+g_2(w_t)+u_t|_{\Gamma}=h(w)&\text{ in }\Gamma\times(0,T),\\[1mm] u=0&\text{ on }\Gamma_0\times(0,T),\\[1mm] \partial_\nu u=w_t&\text{ on }\Gamma\times(0,T),\\[1mm] w=\partial_{\nu_\Gamma}w=0&\text{ on }\partial\Gamma\times(0,T),\\[1mm] (u(0),u_t(0))=(u_0,u_1),\hspace{5mm}(w(0),w_t(0))=(w_0,w_1), \end{cases} \end{align*} where the initial data reside in the finite energy space, i.e., $$(u_0, u_1)\in H^1_{\Gamma_0}(\Omega) \times L^2(\Omega) \, \text{ and }(w_0, w_1)\in H^2_0(\Gamma)\times L^2(\Gamma).$$ The chief assumption of the first model is in taking $f(u)=-u|u|^{p-1}$, i.e., $f$ is a restoring source, where $p\geq 1$ is arbitrary. A standard Galerkin approximation scheme is used to establish a rigorous proof of the existence of local weak solutions. In addition, under some conditions on the parameters in the system, it is shown that such solutions exist globally in time and depend continuously on the initial data. For the second model, $f$ is taken to be an energy building source, and in particular it is allowed to have a \emph{supercritical} exponent, in the sense that its associated Nemytskii operators is not locally Lipschitz from $H^1_{\Gamma_0}(\Omega)$ into $L^2(\Omega)$. By employing nonlinear semigroups and the theory of monotone operators, several results on the existence of local and global weak solutions are obtained. Moreover, it is proven that such solutions depend continuously on the initial data, and uniqueness is obtained in two different scenarios. Adviser: Mohammad A. Rammah

Hadamard Well-Posedness for Two Nonlinear Structure Acoustic Models

This dissertation focuses on the Hadamard well-posedness of two nonlinear structure acoustic models, each consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ strongly coupled with a Berger plate equation acting only on a flat portion of the boundary of $\Omega$. In each case, the PDE is of the following form: \begin{align*} \begin{cases} u_{tt}-\Delta u +g_1(u_t)=f(u) &\text{ in } \Omega \times (0,T),\\[1mm] w_{tt}+\Delta^2w+g_2(w_t)+u_t:_{\Gamma}=h(w)&\text{ in }\Gamma\times(0,T),\\[1mm] u=0&\text{ on }\Gamma_0\times(0,T),\\[1mm] \partial_\nu u=w_t&\text{ on }\Gamma\times(0,T),\\[1mm] w=\partial_{\nu_\Gamma}w=0&\text{ on }\partial\Gamma\times(0,T),\\[1mm] (u(0),u_t(0))=(u_0,u_1),\hspace{5mm}(w(0),w_t(0))=(w_0,w_1), \end{cases} \end{align*} where the initial data reside in the finite energy space, i.e., $$(u_0, u_1)\in H^1_{\Gamma_0}(\Omega) \times L^2(\Omega) \, \text{ and }(w_0, w_1)\in H^2_0(\Gamma)\times L^2(\Gamma).$$ The chief assumption of the first model is in taking $f(u)=-u:u:^{p-1}$, i.e., $f$ is a restoring source, where $p\geq 1$ is arbitrary. A standard Galerkin approximation scheme is used to establish a rigorous proof of the existence of local weak solutions. In addition, under some conditions on the parameters in the system, it is shown that such solutions exist globally in time and depend continuously on the initial data. For the second model, $f$ is taken to be an energy building source, and in particular it is allowed to have a \emph{supercritical} exponent, in the sense that its associated Nemytskii operators is not locally Lipschitz from $H^1_{\Gamma_0}(\Omega)$ into $L^2(\Omega)$. By employing nonlinear semigroups and the theory of monotone operators, several results on the existence of local and global weak solutions are obtained. Moreover, it is proven that such solutions depend continuously on the initial data, and uniqueness is obtained in two different scenarios