Delaunay Ends of Constant Mean Curvature Surfaces

The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal

Plumbophyllite, a new species from the Blue Bell claims near Baker, San Bernardino County, California

The new mineral plumbophyllite, Pb2Si4O10·H2O, orthorhombic with space group Pbcn and cell parameters a = 13.2083(4), b = 9.7832(3), c = 8.6545(2) Å, V = 1118.33(5) Å^3, and Z = 4. It occurs as colorless to pale blue prismatic crystals to 3 mm, with wedge-shaped terminations at the Blue Bell claims, about 11 km west of Baker, San Bernardino County, California. It is found in narrow veins in a highly siliceous hornfels in association with cerussite, chrysocolla, fluorite, goethite, gypsum, mimetite, opal, plumbotsumite, quartz, sepiolite, and wulfenite. The streak is white, the luster is vitreous, the Mohs hardness is about 5, and there is one perfect cleavage, {100}. The measured density is 3.96(5) g/cm^3 and the calculated density is 3.940 g/cm^3. Optical properties (589 nm): biaxial (+), {alpha} = 1.674(2), β = 1.684(2), {gamma} = 1.708(2), 2V = 66(2)°, dispersion r > v (strong); X = b, Y = c, Z = a. Electron microprobe analysis provided PbO 60.25, CuO 0.23, SiO_2 36.22 wt%, and CHN analysis provided H_2O 3.29 wt% for a total of 99.99 wt%. Powder IR spectroscopy confirmed the presence of H_2O and single-crystal IR spectroscopy indicated the H_2O to be oriented perpendicular to the b axis. Raman spectra were also obtained. The strongest powder X-ray diffraction lines are [d (hkl) I]: 7.88(110)97, 6.63(200)35, 4.90(020)38, 3.623(202)100, 3.166(130)45, 2.938(312/411/222)57, 2.555(132/213)51, and 2.243(521/332)50. The atomic structure (R1 = 2.04%) consists of undulating sheets of silicate tetrahedra between which are located Pb atoms and channels containing H_2O (and Pb^(2+) lone-pair electrons). The silicate sheets can be described as consisting of zigzag pyroxene-like (SiO_3)_n chains joined laterally into sheets with the unshared tetrahedral apices in successive chains pointed alternately up and down, a configuration also found in pentagonite

Observation of surface charge screening and Fermi level pinning on a synthetic, boron-doped diamond

Spectroscopic current-voltage (I-V) curves taken with a scanning tunneling microscope on a synthetic, boron-doped diamond single crystal indicate that the diamond, boiled in acid and baked to 500 °C in vacuum, does not exhibit ideal Schottky characteristics. These I-V curves taken in ultrahigh vacuum do not fit the traditional theory of thermionic emission; however, the deviation from ideal can be accounted for by charge screening at the diamond surface. At ambient pressure, the I-V curves have a sharp threshold voltage at 1.7 eV above the valence band edge indicating pinning of the Fermi energy. This measurement is in excellent agreement with the 1/3 band gap rule of Mead and Spitzer [Phys. Rev. 134, A713 (1964)]

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, \bbS^3 and \bbH^3. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.Comment: 18 pages, revised versio

Constant mean curvature surfaces of any positive genus

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.Comment: 14 pages, 10 figure

Photo sensor array technology development

The development of an improved capability photo sensor array imager for use in a Viking '75 type facsimile camera is presented. This imager consists of silicon photodiodes and lead sulfide detectors to cover a spectral range from 0.4 to 2.7 microns. An optical design specifying filter configurations and convergence angles is described. Three electronics design approaches: AC-chopped light, DC-dual detector, and DC-single detector, are investigated. Experimental and calculated results are compared whenever possible using breadboard testing and tolerance analysis techniques. Results show that any design used must be forgiving of the relative instability of lead sulfide detectors. A final design using lead sulfide detectors and associated electronics is implemented by fabrication of a hybrid prototype device. Test results of this device show a good agreement with calculated values

An Interview with Judith M. Conti

...there are many lawyers who look at the law as the limits of what they can do. And instead, I feel like my education taught me to think beyond the limits of what the law is and more about what the law should be and how we can achieve that kind of change. -- Judy Conti. ------------------------------------ This interview took place in the Reeder Media Center at William & Mary on March 8th, 2023, from 2:00 to 3:00 pm. The interview began with Conti discussing her Catholic and liberal upbringing which developed a strong need to give back through public service. She decided that she wanted to go to William & Mary’s Law School because it was a school based on community, rather than competition. She then discussed some of the professors and classes that had the largest impact on Conti as a student. Conti then shares why “Big Law” was not for her and how she knew public service was for her. Conti then covers the revival of the Women’s Law Society as a 1L, co-founding the Journal of Women and the Law, and Professor Jayne Barnard’s advice and encouragement for women in the legal field. Finally, Conti shares about her work after law school, describing cases that inspired her passion for labor and employment law and the co-founding of the DC Employment Justice Center. Conti concludes with remarks about how she continues to carry with her the William & Mary tradition of the citizen lawyer and emphasizing community.https://scholarship.law.wm.edu/oralhist_all/1002/thumbnail.jp

Timescales and mechanisms of formation of amorphous silica coatings on fresh basalts at Kilauea Volcano, Hawai’i

Young basalts from Kilauea Volcano, Hawai'i, frequently feature opaque surface coatings, 1–80 μm thick, composed of amorphous silica and Fe-Ti oxides. These coatings are the product of interaction of the basaltic surface with volcanically-derived acidic fluids. Previous workers have identified these coatings in a variety of contexts on Hawai'i, but the timescales of coating development, coating growth rates, and factors controlling lateral coating heterogeneity were largely unconstrained. We sampled and analyzed young lava flows (of varying ages, from hours to ~ 40 years) along Kilauea's southwest and east rift zones to characterize variation in silica coating properties across the landscape. Coating thickness varies as a function of flow age, flow surface type, and proximity to acid sources like local fissure vents and regional plumes emitted from Kilauea Caldera and Pu'u O'o. Silica coatings that form in immediate proximity to acid sources are more chemically pure than those forming in higher pH environments, which contain significant Al and Fe. Incipient siliceous alteration was observed on basalt surfaces as young as 8 days old, but periods of a year or more are required to develop contiguous coatings with obvious opaque coloration. Inferred coating growth rates vary with environmental conditions but were typically 1-5 μm/year. Coatings form preferentially on flow surfaces with glassy outer layers, such as spatter ramparts, volcanic bombs and dense pahoehoe breakouts, due to glass strain weakening during cooling. Microtextural evidence suggests that the silica coatings form both by in situ dissolution-reprecipitation and by deposition of silica mobilized in solution. Thin films of water, acidified by contact with volcanic vapors, dissolved near-surface basalt, then precipitated amorphous silica in place, mobilizing more soluble cations. Additional silica was transported to and deposited on the surface by silica-bearing altering fluids derived from the basalt interior