Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

Weyl-type Fields with Geodesic Lines of Force

The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have $m>|e|$ or $m<|e|$, but cannot be in the Majumdar-Papapetrou class (in which $m = |e|$). It is algebraically general and has flat equipotential surfaces.Comment: 13 pages, RevTe

Neutral perfect fluids of Majumdar-type in general relativity

We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations, proposed by Ida to include charged perfect fluid sources. We impose the equation of state $\rho+3p=0$ and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges $Q$ and $-Q$. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.Comment: 9 page

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Auxin-Regulated Gene Expression

A number of cDNA clones to independent mRNAs that increase in amount after brief exposure to auxins have been isolated. From soybean, sequenced, and characterized. Increases in mRNA abundance can be detected as early as 2.5 minutes after auxin application to excised elongating regions of soybean hypocotyls. Increased transcription rates on the genes which encode the auxin-responsive mRNAs account, at least partly, for the accumulation of mRNAs. A variety of auxins induce the accumulation of the mRNAs, but other plant hormones have no effect on the mRNA abundance. Some of the genes which encode the mRNAs are clustered in the soybean genome. The soybean gene cluster is expressed under auxin control when transferred into petunia via Agrobacterium T-DNA. In soybean and pea, expression of some of the auxin regulated genes is greatest in the elongating regions of hypocotyl and epicotyl. Some of the genes are primarily expressed in epidermal and outer cortical cells of elongating hypocotyl region. During gravitropism, some of the auxin responsive mRNAs turn over very rapidly and accumulate on the more rapidly elongating side of the hypocotyl

Yang's gravitational theory

Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.Comment: 28 pages, to appear in Gen. Rel. Gra

The Spirit-Murdering of Black Students from White Educators

In this collection of autoethnographies, four researchers explored our deeply personal experiences and encounters with racialized oppression in the form of spirit-murder. Using Critical Race Theory (CRT) and Critical Whiteness Studies, this dissertation explores how two white educators have committed spirit-murder against Black students and how two Black educators have both experienced spirit-murder as students and have spirit-murdered their Black and Brown students as classroom teachers. We wanted to elevate our voices using counter-stories as a tenet of CRT and examples of our teaching practices. We aimed to elicit relatable suggestions to combat spirit-murdering from white educators toward Black students during their grade school and college experiences. All four educators hoped that by sharing, we exposed not only the existence and effects of spirit-murder and ways we were working to eliminate these unfair acts and practices but also ways to better support Black children in classrooms where racist school systems still exist. We reflected on the personal damage caused to us as Black children and created by us towards Black children as white and Black educators. We analyzed the importance and value of a person’s spirit, the term “murder,” and the phrase “spirit-murder,” as they related to our experiences. We shared encounters from grade school to college classrooms in public, private, urban, and suburban settings. Our cohort dissertation group consists of a Black male who is an assistant principal, a white male who is a former visual arts teacher and is now an athletic director, a white female who is a high school English teacher, and a Black female who is a district culture and climate coordinator

Impaired perceptual learning in a mouse model of Fragile X syndrome is mediated by parvalbumin neuron dysfunction and is reversible.

To uncover the circuit-level alterations that underlie atypical sensory processing associated with autism, we adopted a symptom-to-circuit approach in the Fmr1-knockout (Fmr1-/-) mouse model of Fragile X syndrome. Using a go/no-go task and in vivo two-photon calcium imaging, we find that impaired visual discrimination in Fmr1-/- mice correlates with marked deficits in orientation tuning of principal neurons and with a decrease in the activity of parvalbumin interneurons in primary visual cortex. Restoring visually evoked activity in parvalbumin cells in Fmr1-/- mice with a chemogenetic strategy using designer receptors exclusively activated by designer drugs was sufficient to rescue their behavioral performance. Strikingly, human subjects with Fragile X syndrome exhibit impairments in visual discrimination similar to those in Fmr1-/- mice. These results suggest that manipulating inhibition may help sensory processing in Fragile X syndrome