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Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
Description
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Serial femtosecond crystallography requires reliable and efficient delivery of fresh crystals across the beam of an X-ray free-electron laser over the course of an experiment. We introduce a double-flow focusing nozzle to meet this challenge, with significantly reduced sample consumption, while improving jet stability over previous generations of nozzles. We demonstrate its use to determine the first room-temperature structure of RNA polymerase II at high resolution, revealing new structural details. Moreover, the double flow-focusing nozzles were successfully tested with three other protein samples and the first room temperature structure of an extradiol ring-cleaving dioxygenase was solved by utilizing the improved operation and characteristics of these devices.
ContributorsOberthuer, Dominik (Author) / Knoska, Juraj (Author) / Wiedorn, Max O. (Author) / Beyerlein, Kenneth R. (Author) / Bushnell, David A. (Author) / Kovaleva, Elena G. (Author) / Heymann, Michael (Author) / Gumprecht, Lars (Author) / Kirian, Richard (Author) / Barty, Anton (Author) / Mariani, Valerio (Author) / Tolstikova, Aleksandra (Author) / Adriano, Luigi (Author) / Awel, Salah (Author) / Barthelmess, Miriam (Author) / Dorner, Katerina (Author) / Xavier, P. Lourdu (Author) / Yefanov, Oleksandr (Author) / James, Daniel (Author) / Nelson, Garrett (Author) / Wang, Dingjie (Author) / Calvey, George (Author) / Chen, Yujie (Author) / Schmidt, Andrea (Author) / Szczepek, Michael (Author) / Frielingsdorf, Stefan (Author) / Lenz, Oliver (Author) / Snell, Edward (Author) / Robinson, Philip J. (Author) / Sarler, Bozidar (Author) / Belsak, Grega (Author) / Macek, Marjan (Author) / Wilde, Fabian (Author) / Aquila, Andrew (Author) / Boutet, Sebastien (Author) / Liang, Mengning (Author) / Hunter, Mark S. (Author) / Scheerer, Patrick (Author) / Lipscomb, John D. (Author) / Weierstall, Uwe (Author) / Kornberg, Roger D. (Author) / Spence, John (Author) / Pollack, Lois (Author) / Chapman, Henry N. (Author) / Bajt, Sasa (Author) / College of Liberal Arts and Sciences (Contributor) / Department of Physics (Contributor)
Created2017-03-16
Description
X-ray free-electron lasers provide novel opportunities to conduct single particle analysis on nanoscale particles. Coherent diffractive imaging experiments were performed at the Linac Coherent Light Source (LCLS), SLAC National Laboratory, exposing single inorganic core-shell nanoparticles to femtosecond hard-X-ray pulses. Each facetted nanoparticle consisted of a crystalline gold core and a differently shaped palladium shell. Scattered intensities were observed up to about 7 nm resolution. Analysis of the scattering patterns revealed the size distribution of the samples, which is consistent with that obtained from direct real-space imaging by electron microscopy. Scattering patterns resulting from single particles were selected and compiled into a dataset which can be valuable for algorithm developments in single particle scattering research.
ContributorsLi, Xuanxuan (Author) / Chiu, Chun-Ya (Author) / Wang, Hsiang-Ju (Author) / Kassemeyer, Stephan (Author) / Botha, Sabine (Author) / Shoeman, Robert L. (Author) / Lawrence, Robert (Author) / Kupitz, Christopher (Author) / Kirian, Richard (Author) / James, Daniel (Author) / Wang, Dingjie (Author) / Nelson, Garrett (Author) / Messerschmidt, Marc (Author) / Boutet, Sebastien (Author) / Williams, Garth J. (Author) / Hartman, Elisabeth (Author) / Jafarpour, Aliakbar (Author) / Foucar, Lutz M. (Author) / Barty, Anton (Author) / Chapman, Henry (Author) / Liang, Mengning (Author) / Menzel, Andreas (Author) / Wang, Fenglin (Author) / Basu, Shibom (Author) / Fromme, Raimund (Author) / Doak, R. Bruce (Author) / Fromme, Petra (Author) / Weierstall, Uwe (Author) / Huang, Michael H. (Author) / Spence, John (Author) / Schlichting, Ilme (Author) / Hogue, Brenda (Author) / Liu, Haiguang (Author) / ASU Biodesign Center Immunotherapy, Vaccines and Virotherapy (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Molecular Sciences (Contributor) / Department of Physics (Contributor) / School of Life Sciences (Contributor)
Created2017-04-11
Description
Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a well-characterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 μm diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 Ångström were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.
ContributorsMunke, Anna (Author) / Andreasson, Jakob (Author) / Aquila, Andrew (Author) / Awel, Salah (Author) / Ayyer, Kartik (Author) / Barty, Anton (Author) / Bean, Richard J. (Author) / Berntsen, Peter (Author) / Bielecki, Johan (Author) / Boutet, Sebastien (Author) / Bucher, Maximilian (Author) / Chapman, Henry N. (Author) / Daurer, Benedikt J. (Author) / DeMirci, Hasan (Author) / Elser, Veit (Author) / Fromme, Petra (Author) / Hajdu, Janos (Author) / Hantke, Max F. (Author) / Higashiura, Akifumi (Author) / Hogue, Brenda (Author) / Hosseinizadeh, Ahmad (Author) / Kim, Yoonhee (Author) / Kirian, Richard (Author) / Reddy, Hemanth K. N. (Author) / Lan, Ti-Yen (Author) / Larsson, Daniel S. D. (Author) / Liu, Haiguang (Author) / Loh, N. Duane (Author) / Maia, Filipe R. N. C. (Author) / Mancuso, Adrian P. (Author) / Muhlig, Kerstin (Author) / Nakagawa, Atsushi (Author) / Nam, Daewoong (Author) / Nelson, Garrett (Author) / Nettelblad, Carl (Author) / Okamoto, Kenta (Author) / Ourmazd, Abbas (Author) / Rose, Max (Author) / van der Schot, Gijs (Author) / Schwander, Peter (Author) / Seibert, M. Marvin (Author) / Sellberg, Jonas A. (Author) / Sierra, Raymond G. (Author) / Song, Changyong (Author) / Svenda, Martin (Author) / Timneanu, Nicusor (Author) / Vartanyants, Ivan A. (Author) / Westphal, Daniel (Author) / Wiedom, Max O. (Author) / Williams, Garth J. (Author) / Xavier, Paulraj Lourdu (Author) / Soon, Chun Hong (Author) / Zook, James (Author) / College of Liberal Arts and Sciences (Contributor, Contributor) / School of Molecular Sciences (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / School of Life Sciences (Contributor) / Infectious Diseases and Vaccinology (Contributor) / Department of Physics (Contributor)
Created2016-08-01
Description
Serial femtosecond X-ray crystallography (SFX) using an X-ray free electron laser (XFEL) is a recent advancement in structural biology for solving crystal structures of challenging membrane proteins, including G-protein coupled receptors (GPCRs), which often only produce microcrystals. An XFEL delivers highly intense X-ray pulses of femtosecond duration short enough to enable the collection of single diffraction images before significant radiation damage to crystals sets in. Here we report the deposition of the XFEL data and provide further details on crystallization, XFEL data collection and analysis, structure determination, and the validation of the structural model. The rhodopsin-arrestin crystal structure solved with SFX represents the first near-atomic resolution structure of a GPCR-arrestin complex, provides structural insights into understanding of arrestin-mediated GPCR signaling, and demonstrates the great potential of this SFX-XFEL technology for accelerating crystal structure determination of challenging proteins and protein complexes.
ContributorsZhou, X. Edward (Author) / Gao, Xiang (Author) / Barty, Anton (Author) / Kang, Yanyong (Author) / He, Yuanzheng (Author) / Liu, Wei (Author) / Ishchenko, Andrii (Author) / White, Thomas A. (Author) / Yefanov, Oleksandr (Author) / Han, Gye Won (Author) / Xu, Qingping (Author) / de Waal, Parker W. (Author) / Suino-Powell, Kelly M. (Author) / Boutet, Sebastien (Author) / Williams, Garth J. (Author) / Wang, Meitian (Author) / Li, Dianfan (Author) / Caffrey, Martin (Author) / Chapman, Henry N. (Author) / Spence, John (Author) / Fromme, Petra (Author) / Weierstall, Uwe (Author) / Stevens, Raymond C. (Author) / Cherezov, Vadim (Author) / Melcher, Karsten (Author) / Xu, H. Eric (Author) / College of Liberal Arts and Sciences (Contributor) / School of Molecular Sciences (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / Department of Physics (Contributor)
Created2016-04-12
Description
Diacylglycerol kinase catalyses the ATP-dependent conversion of diacylglycerol to phosphatidic acid in the plasma membrane of Escherichia coli. The small size of this integral membrane trimer, which has 121 residues per subunit, means that available protein must be used economically to craft three catalytic and substrate-binding sites centred about the membrane/cytosol interface. How nature has accomplished this extraordinary feat is revealed here in a crystal structure of the kinase captured as a ternary complex with bound lipid substrate and an ATP analogue. Residues, identified as essential for activity by mutagenesis, decorate the active site and are rationalized by the ternary structure. The γ-phosphate of the ATP analogue is positioned for direct transfer to the primary hydroxyl of the lipid whose acyl chain is in the membrane. A catalytic mechanism for this unique enzyme is proposed. The active site architecture shows clear evidence of having arisen by convergent evolution.
ContributorsLi, Dianfan (Author) / Stansfeld, Phillip J. (Author) / Sansom, Mark S. P. (Author) / Keogh, Aaron (Author) / Vogeley, Lutz (Author) / Howe, Nicole (Author) / Lyons, Joseph A. (Author) / Aragao, David (Author) / Fromme, Petra (Author) / Fromme, Raimund (Author) / Basu, Shibom (Author) / Grotjohann, Ingo (Author) / Kupitz, Christopher (Author) / Rendek, Kimberley (Author) / Weierstall, Uwe (Author) / Zatsepin, Nadia (Author) / Cherezov, Vadim (Author) / Liu, Wei (Author) / Bandaru, Sateesh (Author) / English, Niall J. (Author) / Gati, Cornelius (Author) / Barty, Anton (Author) / Yefanov, Oleksandr (Author) / Chapman, Henry N. (Author) / Diederichs, Kay (Author) / Messerschmidt, Marc (Author) / Boutet, Sebastien (Author) / Williams, Garth J. (Author) / Seibert, M. Marvin (Author) / Caffrey, Martin (Author) / College of Liberal Arts and Sciences (Contributor) / School of Molecular Sciences (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / Department of Physics (Contributor)
Created2015-12-17
Description
Phytochromes are a family of photoreceptors that control light responses of plants, fungi and bacteria. A sequence of structural changes, which is not yet fully understood, leads to activation of an output domain. Time-resolved serial femtosecond crystallography (SFX) can potentially shine light on these conformational changes. Here we report the room temperature crystal structure of the chromophore-binding domains of the Deinococcus radiodurans phytochrome at 2.1 Å resolution. The structure was obtained by serial femtosecond X-ray crystallography from microcrystals at an X-ray free electron laser. We find overall good agreement compared to a crystal structure at 1.35 Å resolution derived from conventional crystallography at cryogenic temperatures, which we also report here. The thioether linkage between chromophore and protein is subject to positional ambiguity at the synchrotron, but is fully resolved with SFX. The study paves the way for time-resolved structural investigations of the phytochrome photocycle with time-resolved SFX.
ContributorsEdlund, Petra (Author) / Takala, Heikki (Author) / Claesson, Elin (Author) / Henry, Leocadie (Author) / Dods, Robert (Author) / Lehtivuori, Heli (Author) / Panman, Matthijs (Author) / Pande, Kanupriya (Author) / White, Thomas (Author) / Nakane, Takanori (Author) / Berntsson, Oskar (Author) / Gustavsson, Emil (Author) / Bath, Petra (Author) / Modi, Vaibhav (Author) / Roy Chowdhury, Shatabdi (Author) / Zook, James (Author) / Berntsen, Peter (Author) / Pandey, Suraj (Author) / Poudyal, Ishwor (Author) / Tenboer, Jason (Author) / Kupitz, Christopher (Author) / Barty, Anton (Author) / Fromme, Petra (Author) / Koralek, Jake D. (Author) / Tanaka, Tomoyuki (Author) / Spence, John (Author) / Liang, Mengning (Author) / Hunter, Mark S. (Author) / Boutet, Sebastien (Author) / Nango, Eriko (Author) / Moffat, Keith (Author) / Groenhof, Gerrit (Author) / Ihalainen, Janne (Author) / Stojkovic, Emina A. (Author) / Schmidt, Marius (Author) / Westenhoff, Sebastian (Author) / College of Liberal Arts and Sciences (Contributor) / School of Molecular Sciences (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / Department of Physics (Contributor)
Created2016-10-19
Description
Serial femtosecond crystallography (SFX) using X-ray free-electron laser sources is an emerging method with considerable potential for time-resolved pump-probe experiments. Here we present a lipidic cubic phase SFX structure of the light-driven proton pump bacteriorhodopsin (bR) to 2.3 Å resolution and a method to investigate protein dynamics with modest sample requirement. Time-resolved SFX (TR-SFX) with a pump-probe delay of 1 ms yields difference Fourier maps compatible with the dark to M state transition of bR. Importantly, the method is very sample efficient and reduces sample consumption to about 1 mg per collected time point. Accumulation of M intermediate within the crystal lattice is confirmed by time-resolved visible absorption spectroscopy. This study provides an important step towards characterizing the complete photocycle dynamics of retinal proteins and demonstrates the feasibility of a sample efficient viscous medium jet for TR-SFX.
ContributorsNogly, Przemyslaw (Author) / Panneels, Valerie (Author) / Nelson, Garrett (Author) / Gati, Cornelius (Author) / Kimura, Tetsunari (Author) / Milne, Christopher (Author) / Milathianaki, Despina (Author) / Kubo, Minoru (Author) / Wu, Wenting (Author) / Conrad, Chelsie (Author) / Coe, Jesse (Author) / Bean, Richard (Author) / Zhao, Yun (Author) / Bath, Petra (Author) / Dods, Robert (Author) / Harimoorthy, Rajiv (Author) / Beyerlein, Kenneth R. (Author) / Rheinberger, Jan (Author) / James, Daniel (Author) / Deponte, Daniel (Author) / Li, Chufeng (Author) / Sala, Leonardo (Author) / Williams, Garth J. (Author) / Hunter, Mark S. (Author) / Koglin, Jason E. (Author) / Berntsen, Peter (Author) / Nango, Eriko (Author) / Iwata, So (Author) / Chapman, Henry N. (Author) / Fromme, Petra (Author) / Frank, Matthias (Author) / Abela, Rafael (Author) / Boutet, Sebastien (Author) / Barty, Anton (Author) / White, Thomas A. (Author) / Weierstall, Uwe (Author) / Spence, John (Author) / Neutze, Richard (Author) / Schertler, Gebhard (Author) / Standfuss, Jorg (Author) / College of Liberal Arts and Sciences (Contributor) / Department of Physics (Contributor) / Department of Chemistry and Biochemistry (Contributor) / Biodesign Institute (Contributor) / Applied Structural Discovery (Contributor) / School of Molecular Sciences (Contributor)
Created2016-08-22