A Peak Point Theorem for Uniform Algebras on Real-Analytic Varieties

It was once conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$, and if each point of $X$ is a peak point for $A$, then $A = C(X)$. This peak-point conjecture was disproved by Brian Cole in 1968. Here we establish a peak-point theorem for uniform algebras generated by real-analytic functions on real-analytic varieties, generalizing previous results of the authors and John Wermer

Synthesis and Characterization of Three-Coordinate Ni(III)-Imide Complexes

A new family of low-coordinate nickel imides supported by 1,2-bis(di-tert-butylphosphino)ethane was synthesized. Oxidation of nickel(II) complexes led to the formation of both aryl- and alkyl-substituted nickel(III)-imides, and examples of both types have been isolated and fully characterized. The aryl substituent that proved most useful in stabilizing the Ni(III)-imide moiety was the bulky 2,6-dimesitylphenyl. The two Ni(III)-imide compounds showed different variable-temperature magnetic properties but analogous EPR spectra at low temperatures. To account for this discrepancy, a low-spin/high-spin equilibrium was proposed to take place for the alkyl-substituted Ni(III)-imide complex. This proposal was supported by DFT calculations. DFT calculations also indicated that the unpaired electron is mostly localized on the imide nitrogen for the Ni(III) complexes. The results of reactions carried out in the presence of hydrogen donors supported the findings from DFT calculations that the adamantyl substituent was a significantly more reactive hydrogen-atom abstractor. Interestingly, the steric properties of the 2,6-dimesitylphenyl substituent are important not only in protecting the Ni═N core but also in favoring one rotamer of the resulting Ni(III)-imide, by locking the phenyl ring in a perpendicular orientation with respect to the NiPP plane

Low- and high-frequency noise from coherent two-level systems

Recent experiments indicate a connection between the low- and high-frequency noise affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g., by sufficiently coherent two-level systems (TLS). This implies a relation between the noise power in different frequency domains, which depends on the distribution of the parameters of the TLSs. We show that a distribution, natural for tunneling TLSs, with a log-uniform distribution in the tunnel splitting and linear distribution in the bias, accounts for experimental observations.Comment: minor corrections, references adde

Electric field effect on superconductivity at complex oxide interfaces

We examine the enhancement of the interfacial superconductivity between LaAlO$_{3}$ and SrTiO$_{3}$ by an effective electric field. Through the breaking of inversion symmetry at the interface, we show that a term coupling the superfluid density and an electric field can augment the superconductivity transition temperature. Microscopically, we show that an electric field can also produce changes in the carrier density by relating the measured capacitance to the density of states. Through the electron-phonon induced interaction in bulk SrTiO$_{3}$, we estimate the transition temperature.Comment: 7 Pages, Submitted to Physical Revie

New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.Comment: 11 page

Fluid-Induced Propulsion of Rigid Particles in Wormlike Micellar Solutions

In the absence of inertia, a reciprocal swimmer achieves no net motion in a viscous Newtonian fluid. Here, we investigate the ability of a reciprocally actuated particle to translate through a complex fluid that possesses a network using tracking methods and birefringence imaging. A geometrically polar particle, a rod with a bead on one end, is reciprocally rotated using magnetic fields. The particle is immersed in a wormlike micellar (WLM) solution that is known to be susceptible to the formation of shear bands and other localized structures due to shear-induced remodeling of its microstructure. Results show that the nonlinearities present in this WLM solution break time-reversal symmetry under certain conditions, and enable propulsion of an artificial "swimmer." We find three regimes dependent on the Deborah number (De): net motion towards the bead-end of the particle at low De, net motion towards the rod-end of the particle at intermediate De, and no appreciable propulsion at high De. At low De, where the particle time-scale is longer then the fluid relaxation time, we believe that propulsion is caused by an imbalance in the fluid first normal stress differences between the two ends of the particle (bead and rod). At De~1, however, we observe the emergence of a region of network anisotropy near the rod using birefringence imaging. This anisotropy suggests alignment of the micellar network, which is "locked in" due to the shorter time-scale of the particle relative to the fluid

Triangleland. I. Classical dynamics with exchange of relative angular momentum

In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics from relational premises. This is of interest in the absolute versus relative motion debate and also shares a number of features with the geometrodynamical formulation of general relativity, making it suitable for some modelling of the problem of time in quantum gravity. I also study similarity relational particle mechanics (`dynamics of pure shape'), in which only relative times, relative angles and {\sl ratios of} relative separations are meaningful. This I consider firstly as it is simpler, particularly in 1 and 2 d, for which the configuration space geometry turns out to be well-known, e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail. Secondly, the similarity model occurs as a sub-model within the Euclidean model: that admits a shape--scale split. For harmonic oscillator like potentials, similarity triangleland model turns out to have the same mathematics as a family of rigid rotor problems, while the Euclidean case turns out to have parallels with the Kepler--Coulomb problem in spherical and parabolic coordinates. Previous work on relational mechanics covered cases where the constituent subsystems do not exchange relative angular momentum, which is a simplifying (but in some ways undesirable) feature paralleling centrality in ordinary mechanics. In this paper I lift this restriction. In each case I reduce the relational problem to a standard one, thus obtain various exact, asymptotic and numerical solutions, and then recast these into the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure