Casimir probe based upon metallized high Q SiN nanomembrane resonator

We present the instrumentation and measurement scheme of a new Casimir force probe that bridges Casimir force measurements at microscale and macroscale. A metallized high Q silicon nitride nanomembrane resonator is employed as a sensitive force probe. The high tensile stress present in the nanomembrane not only enhances the quality factor but also maintains high flatness over large area serving as the bottom electrode in a sphere-plane configuration. A fiber interferometer is used to readout the oscillation of the nanomembrane and a phase-locked loop scheme is applied to track the change of the resonance frequency. Because of the high quality factor of the nanomembrane and the high stability of the setup, a frequency resolution down to $2\times10^{-9}$ and a corresponding force gradient resolution of 3 $\mu$N/m is achieved. Besides sensitive measurement of Casimir force, our measurement technique simultaneously offers Kelvin probe measurement capability that allows in situ imaging of the surface potentials

Seats, Votes, and Gerrymandering: Estimating Representation and Bias in State Legislative Redistricting

The Davis V. Bandemer case focused much attention on the problem of using statistical evidence to demonstrate the existence of political gerrymandering. In this paper, we evaluate the uses and limitations of measures of the seat-votes relationship in the Bandemer case. We outline a statistical method we have developed that can be used to estimate bias and the form of representation in legislative redistricting. We apply this method to Indiana state House and Senate elections for the period 1972 to 1984 and demonstrate a maximum bias of 6.2% toward the Republicans in the House and a 2.8% bias in the Senate.Governmen

Democratic Representation and Partisan Bias in Congressional Elections

T h e translation of citizen votes into legislative seats is of central importance in democratic electoral systems. It has been a longstanding concern among scholars in political science and in numerous other disciplines. Throughout this literature, two fundamental tenets of democratic theory, partisan bias and democratic representation, have often been confused. We develop a general statistical model of the relationship between votes and seats and separate these two important concepts theoretically and empirically. In so doing, we also solve several methodological problems with the study of seats, votes, and the cube law. An application to U.S. congressional districts provides estimates of bias and representation for each state and demonstrates the model's utility. Results of this application show distinct types of representation coexisting in U.S. states. Although most states have small partisan biases, there are some with a substantial degree of bias.Governmen

Relationship structure-antioxidant activity of hindered phenolic compounds

The relationship between the structure and the antioxidant activity of 21 hindered phenolic compounds was investigated by Rancimat and DPPH· tests. 3-<em>tert</em>-butyl-5-methylbenzene-1,2-diol is the strongest antioxidant in the Rancimat test but not in the DPPH· test because its two hydroxyl groups have very strong steric synergy. 2,6-Di<em>tert</em>-butyl-4-hydroxy-methylphenol exhibits a strong antioxidant activity as 2,6-di<em>tert</em>butyl- 4-methoxyphenol does in lard. 2,6-Di<em>tert</em>-butyl-4- hydroxy-methylphenol also exhibits stronger activity than 2-<em>tert</em>-butyl-4- methoxyphenol. The methylene of 2,6-di<em>tert</em>-butyl-4-hydroxy-methylphenol can provide a hydrogen atom to active free radicals like a phenolic hydroxyl group does because it is greatly activated by both the aromatic ring and hydroxyl group. Five factors affect the antioxidant activities of the phenolic compounds: how stable the phenolic compound free radicals are after providing hydrogen atoms; how many hy drogen atoms each of the phenolic compounds can provide; how fast the phenolic compounds provide hydrogen atoms; how easily the phenolic compound free radicals can combine with more active free radicals, and whether or not a new antioxidant can form after the phenolic compound provides hydrogen atoms.<br><br>La relación entre estructura y la actividad antioxidante de 21 compuestos fenólicos con impedimentos estéricos fue investigado mediante ensayos con Rancimat y DPPH·. El 3-<em>terc</em>-butil-5-metilbenceno-1,2-diol es el antioxidante más potente en los ensayos mediante Rancimat pero no mediante ensayos con DPPH·, porque sus dos grupos hidroxilo tienen una fuerte sinergia estérica. El 2,6-Di-<em>terc</em>-butil-4-hidroxi-metil-fenol mostró una actividad antioxidante tan fuerte como el 2,6-di-ter-butil-4-metoxifenol en ensayos con manteca de cerdo. El 2,6-di-<em>terc</em>-butil-4-hidroxi-metilfenol también mostró una actividad más fuerte que el 2-<em>terc</em>-butil-4-metoxifenol. El grupo metileno del 2,6-di-ter-butil-4-hidroxi-metilfenol puede suministrar átomos de hidrógeno y activar radicales libres como lo hace un grupo hidroxilo fenólico porque se activa en gran medida tanto por anillo aromático como por el grupo hidroxilo. Cinco factores afectan a la actividad antioxidante de los compuestos fenólicos: cómo de estable son los radicales libres de los compuestos fenólicos después de suministrar átomos de hidrógeno; cuántos átomos de hidrógeno pueden proporcionar cada uno de los compuestos fenólicos; la rapidez con la que los compuestos fenólicos donen átomos de hidrógeno; la facilidad con la que los radicales libres de los compuestos fenólicos pueden combinarse con los radicales libres más activos, y si es o no un nuevo antioxidante el que se puede formar después de que el compuesto fenólico done los átomos de hidrógeno

Nonlocality of Kohn-Sham exchange-correlation fields in dielectrics

The theory of the macroscopic field appearing in the Kohn-Sham exchange-correlation potential for dielectric materials, as introduced by Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field cannot be determined from a knowledge of the local state of the material (local crystal potential, electric field, and polarization) alone. Instead, it has an intrinsically nonlocal dependence on the global electrostatic configuration. For example, it vanishes in simple transverse configurations of a polarized dielectric, but not in longitudinal ones.Comment: 4 pages, two-column style with 2 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#dv_gg

Electron localization : band-by-band decomposition, and application to oxides

Using a plane wave pseudopotential approach to density functional theory we investigate the electron localization length in various oxides. For this purpose, we first set up a theory of the band-by-band decomposition of this quantity, more complex than the decomposition of the spontaneous polarization (a related concept), because of the interband coupling. We show its interpretation in terms of Wannier functions and clarify the effect of the pseudopotential approximation. We treat the case of different oxides: BaO, $\alpha$-PbO, BaTiO$_3$ and PbTiO$_3$. We also investigate the variation of the localization tensor during the ferroelectric phase transitions of BaTiO$_3$ as well as its relationship with the Born effective charges