Global well-posedness for the dynamical Q-tensor model of liquid crystals

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions

Beyond Minimal Lepton Flavored Dark Matter

We consider a class of flavored dark matter (DM) theories where dark matter interacts with the Standard Model lepton fields at the renormalizable level. We allow for a general coupling matrix between the dark matter and leptons whose structure is beyond the one permitted by the minimal flavor violation (MFV) assumption. It is assumed that this is the only new source of flavor violation in addition to the Standard Model (SM) Yukawa interactions. The setup can be described by augmenting the SM flavor symmetry by an additional $\mathrm{SU}(3)_{\chi}$, under which the dark matter $\chi$ transforms. This framework is especially phenomenologically rich, due to possible novel flavor-changing interactions which are not present within the more restrictive MFV framework. As a representative case study of this setting, which we call "beyond MFV" (BMFV), we consider Dirac fermion dark matter which transforms as a singlet under the SM gauge group and a triplet under $\mathrm{SU}(3)_{\chi}$. The DM fermion couples to the SM lepton sector through a scalar mediator $\phi$. Unlike the case of quark-flavored DM, we show that there is no $\mathbb{Z}_3$ symmetry within either the MFV or BMFV settings which automatically stabilizes the lepton-flavored DM. We discuss constraints on this setup from flavor-changing processes, DM relic abundance as well as direct and indirect detections. We find that relatively large flavor-changing couplings are possible, while the dark matter mass is still within the phenomenologically interesting region below the TeV scale. Collider signatures which can be potentially searched for at the lepton and hadron colliders are discussed. Finally, we discuss the implications for decaying dark matter, which can appear if an additional stabilizing symmetry is not imposed.Comment: 30 pages, 12 figures; minor corrections, added references and discussion on decaying dark matter, matches published versio

Molecular Evolutionary Studies using Structural Genomics and Proteomics.

The field of molecular evolution has progressed with the accumulation of various molecular data. It started with the analysis of protein sequence data, followed by that of gene and genome sequence dada. Recently, structural genomics and proteomics have offered new types of data for addressing molecular evolution questions. Structural genomics refers to genome-wide collection of protein structures, whereas proteomics is the study of all proteins in a cell or organism. In this thesis, I conducted molecular evolutionary projects using data provided by structural genomics and proteomics. First, I used protein structure information to explain why some human-disease associated amino acid residues (DARs) appear as the wild-type in other species. Because destabilizing protein structures is a primary reason why DARs are deleterious, I focused on protein stability and discovered that, in species where a DAR represents the wild-type, the destabilizing effect of the DAR is generally lessened by the observed amino acid substitutions in the spatial proximity of the DAR. This finding of compensatory residue substitutions has important implications for understanding epistasis in protein evolution. Second, the recently published human proteomes include peptides encoded by annotated pseudogenes, which are relics of formerly functional genes. These translated pseudogenes may actually be functional and subject to purifying selection. Alternatively, their translations may be accidental and do not indicate functionality. My analysis suggests that a sizable fraction of the translated pseudogenes are subject to purifying selection acting at the protein level. Third, for the purpose of understanding protein evolution and structure-function relationships, protein structures are classified according to their structure similarities. A fold encompasses protein structures with similar core topologies. Current fold classifications implicitly assume that folds are discrete islands in the protein structure space, whereas increasing evidence supports a continuous fold space. I developed a likelihood method to classify structures into existing folds by considering the continuity in fold space. My results using this method demonstrated the growing importance of considering this continuity in fold classification. Together, my work illustrated the utility of structural genomics and proteomics in answering evolutionary questions and provided better understanding of gene and protein evolution.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113597/1/jinruixu_1.pd

Collisions of Jets of Particles from Active Galactic Nuclei with Neutralino Dark Matter

We examine the possibility that energetic Standard Model particles contained in the jets produced by active galactic nuclei (AGN) may scatter off of the dark matter halo which is expected to surround the AGN. In particular, if there are nearby states in the dark sector which can appear resonantly in the scattering, the cross section can be enhanced and a distinctive edge feature in the energy spectrum may appear. We examine bounds on supersymmetric models which may be obtained from the Fermi Gamma-ray Space Telescope observation of the nearby AGN Centaurus A.Comment: 20 pages, 9 figures; v2: version published in JCA

University tutors’ beliefs about and practices in assessing undergraduates’ writing - A New Zealand case study

Although teacher cognition has been explored widely, university tutor cognition of professional activities, such as evaluating and giving written feedback on students’ written work, has rarely been explored. Very few studies on teacher cognition of giving feedback have included data of real practice collected by think-aloud, observation, and stimulated recall. Traditional teacher cognition studies mainly focus on individual teachers’ beliefs and practices without in-depth study on how individual cognition evolves through and interacts with its social context in which individual teachers participate. It is the research space above that this thesis seeks to occupy, through an in-depth case study of the beliefs and practices of sixteen New Zealand university tutors who were employed in one of the university’s faculties to provide feedback on undergraduates’ assignments. In addition to exploring the beliefs and practices of this specific group of tutors, and the factors that influence these, the study aims to contribute to both the theoretical and methodological construction of teacher cognition studies by employing a holistic socio-cultural frame work based on Vygotsky’ s key notions of cognition, distributed cognition, and an activity theory approach. Data were collected chronologically across an academic year by five methods: preliminary survey for bio-data of participants and their general attitudes to giving feedback across the faculty, individual interviews for beliefs on giving feedback, think-aloud sessions on the actual practice of giving feedback, stimulated recall discussions as reflection in action, and focus group discussion as a means of collective reflection of various factors underlying their beliefs and practices. Data were firstly transcribed, stored, and open coded by NVivo8 for preliminary analysis and then analysed manually for deeper understanding of themes. Constant comparisons were made through the whole process of data analysis between data from different participants and between different sources of data. The findings reveal that there were convergences and divergences among tutors between their beliefs and practices about providing assessment feedback to the written work by undergraduate students. The convergences and divergences were due to the contextual factors in the activity system and tutors' previous experiences. The convergences and divergences of tutors’ beliefs resulted in emotional reactions. Tutors’ emotion interacts with cognition and actions (ECA interaction). The ECA interaction is affected by contextual factors in the activity system. The contradictions of the activity system constrain tutors’ cognition, cause negative emotions, and are often barriers to tutors’ work, but also form the potential of cognitive development. Co-operative effort is needed in the wider context of the activity to facilitate tutors’ cognitive development, promote positive emotions, and achieve a better outcome for the activity. It is concluded that a holistic socio-cultural framework of teacher cognition contributes to the understanding of the complexity of teacher cognition. The study is significant for its practical implications for professional practice of assessing disciplinary writing and tutor development; its contribution to the development of teacher cognition and activity theory regarding the interaction between emotion, cognition, and action at both individual and distributed level; and a multi-method approach to teacher cognition studies