Panel collapse and its applications

We describe a procedure called panel collapse for replacing a CAT(0) cube complex $\Psi$ by a "lower complexity" CAT(0) cube complex $\Psi_\bullet$ whenever $\Psi$ contains a codimension-$2$ hyperplane that is extremal in one of the codimension-$1$ hyperplanes containing it. Although $\Psi_\bullet$ is not in general a subcomplex of $\Psi$, it is a subspace consisting of a subcomplex together with some cubes that sit inside $\Psi$ "diagonally". The hyperplanes of $\Psi_\bullet$ extend to hyperplanes of $\Psi$. Applying this procedure, we prove: if a group $G$ acts cocompactly on a CAT(0) cube complex $\Psi$, then there is a CAT(0) cube complex $\Omega$ so that $G$ acts cocompactly on $\Omega$ and for each hyperplane $H$ of $\Omega$, the stabiliser in $G$ of $H$ acts on $H$ essentially. Using panel collapse, we obtain a new proof of Stallings's theorem on groups with more than one end. As another illustrative example, we show that panel collapse applies to the exotic cubulations of free groups constructed by Wise. Next, we show that the CAT(0) cube complexes constructed by Cashen-Macura can be collapsed to trees while preserving all of the necessary group actions. (It also illustrates that our result applies to actions of some non-discrete groups.) We also discuss possible applications to quasi-isometric rigidity for certain classes of graphs of free groups with cyclic edge groups. Panel collapse is also used in forthcoming work of the first-named author and Wilton to study fixed-point sets of finite subgroups of $\mathrm{Out}(F_n)$ on the free splitting complex. Finally, we apply panel collapse to a conjecture of Kropholler, obtaining a short proof under a natural extra hypothesis.Comment: Revised according to referee comments. This version accepted in "Groups, Geometry, and Dynamics

Strong Hall voltage modulation in hybrid ferromagnet/semiconductor microstructures

We present a new magnetoelectronic device consisting of a µm-scale semiconductor cross junction and a patterned, electrically isolated, ferromagnetic overlayer with in-plane magnetization. The large local magnetic field emanating from the edge of the thin ferromagnetic film has a strong perpendicular magnetic component, B[perpendicular](r), which induces a Hall resistance, RH, in the microjunction. External application of a weak in-plane magnetic field reverses the magnetization of the ferromagnet and with it B[perpendicular](r), thus modulating RH. Our data demonstrate that this strong "local" Hall effect is operative at both cryogenic and room temperatures, and is promising for device applications such as field sensors or integrated nonvolatile memory cells

Modeling vitreous silica bilayers

We computer model a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. Here we model the bilayer using a computer assembly procedure that starts from a single layer of amorphous graphene, generated using a bond switching algorithm from an initially crystalline graphene structure. Next each bond is decorated with an oxygen atom and the carbon atoms are relabeled as silicon. This monolayer can be now thought of as a two dimensional network of corner sharing triangles. Next each triangle is made into a tetrahedron, by raising the silicon atom above each triangle and adding an additional singly coordinated oxygen atom at the apex. The final step is to mirror reflect this layer to form a second layer and then attach the two layers together to form the bilayer. We show that this vitreous silica bilayer has the additional macroscopic degrees of freedom to easily form a network of identical corner sharing tetrahedra if there is a symmetry plane through the center of the bilayer going through the layer of oxygen ions that join the upper and lower layers. This has the consequence that the upper rings lie exactly above the lower rings, which are tilted in general. The assumption of a network of perfect corner sharing tetrahedra leads to a range of possible densities that we have previously characterized in three dimensional zeolites as a flexibility window. Finally, using a realistic potential, we have relaxed the bilayer to determine the density, and other structural characteristics such as the Si-Si pair distribution functions and the Si-O-Si bond angle distribution, which are compared to the experimental results obtained by direct imaging

Influence of low and high pressure baroreceptors on plasma renin activity in humans

The effects of low and high pressure baroreceptors on plasma renin activity (immunoassay) were evaluated using graded lower body suction (LBS) in six healthy men. LBS at -10 and -20 mmHg for 10 min decreased central venous pressure without changing arterial pressure and thereby presumably reduced low but not high pressure baroreceptor inhibition of renin release. LBS at these levels produced forearm vasoconstriction, but did not increase renin. LBS at -40 mmHG decreased central venous and arterial pulse pressure and thus reduced both low and high pressure baroreceptor inhibition. LBS at this level produced forearm vasoconstriction and tachycardia and increased renin. In summary, reduction in low pressure baroreceptor inhibition in humans did not increase renin in the presence of physiological tonic inhibition from high pressure baroreceptors. Increases in renin did not occur until there was combined reduction of high and low pressure baroreceptor inhibition on plasma renin activity

Key results of the mini-dome Fresnel lens concentrator array development program under recently completed NASA and SDIO SBIR projects

Since 1986, ENTECH and the NASA Lewis Research Center have been developing a new photovoltaic concentrator system for space power applications. The unique refractive system uses small, dome shaped Fresnel lenses to focus sunlight onto high efficiency photovoltaic concentrator cells which use prismatic cell covers to further increase their performance. Highlights of the five-year development include near Air Mass Zero (AM0) Lear Jet flight testing of mini-dome lenses (90 pct. net optical efficiency achieved); tests verifying sun-pointing error tolerance with negligible power loss; simulator testing of prism-covered GaAs concentrator cells (24 pct. AM0 efficiency); testing of prism-covered Boeing GaAs/GaSb tandem cells (31 pct. AM0 efficiency); and fabrication and outdoor testing of a 36-lens/cell element panel. These test results have confirmed previous analytical predictions which indicate substantial performance improvements for this technology over current array systems. Based on program results to date, it appears than an array power density of 300 watts/sq m and a specific power of 100 watts/kg can be achieved in the near term. All components of the array appear to be readily manufacturable from space-durable materials at reasonable cost. A concise review is presented of the key results leading to the current array, and further development plans for the future are briefly discussed

Cubulating hyperbolic free-by-cyclic groups: the general case

Let $\Phi:F\rightarrow F$ be an automorphism of the finite-rank free group $F$. Suppose that $G=F\rtimes_\Phi\mathbb Z$ is word-hyperbolic. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.Comment: 36 pages, 11 figures. Version 2 contains minor corrections. Accepted to GAF