Double potential step chronoamperometry at a microband electrode: Theory and experiment

Numerical simulation is used to characterise double potential step chronoamperometry at a microband electrode for a simple redox process A + e- goes to B, under conditions of full support such that diffusion is the only active form of mass transport. The method is shown to be highly sensitive for the measurement of the diffusion coefficient of both A and B, and is applied to the one electron reduction of decamethylferrocene (DMFc), DMFc - e- goes to DMFc+, in the room temperature ionic liquid 1-propyl-3-methylimidazolium bistrifluoromethylsulfonylimide. Theory and experiment are seen to be in excellent agreement and the following values of the diffusion coefficients were measured at 298 K: D_(DMFc) = 2.50 x 10^(-7) cm^(2) s^(-1) and D_(DMFc+) = 9.50 x 10^(-8) cm^(2) s^(-1)

Sunjammer

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The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.Comment: 10 page

QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime

An integral solution to the quantum Knizhnik-Zamolodchikov ($q$KZ) equation with $|q|=1$ is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest neighbor correlator with an arbitrary coupling constant, and general correlators in the XXX and XY limits

A classification of spherically symmetric spacetimes

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A variety of physically meaningful example spacetimes are discussed

Students' mental prototypes for functions and graphs

This research study investigates the concept of function developed by students studying English A-level mathematics. It shows that, while students may be able to use functions in their practical mathematics, their grasp of the theoretical nature of the function concept may be tenuous and inconsistent. The hypothesis is that students develop prototypes for the function concept in much the same way as they develop prototypes for concepts in everyday life. The definition of the function concept, though given in the curriculum, is not stressed and proves to be inoperative, with their understanding of the concept reliant on properties of familiar prototype examples: those having regular shaped graphs, such as x2 or sin*, those often encountered (possibly erroneously), such as a circle, those in which y is defined as an explicit formula in x, and so on. Investigations reveal significant misconceptions. For example, threequarters of a sample of students starting a university mathematics course considered that a constant function was not a function in either its graphical or algebraic forms, and threequarters thought that a circle is a function. This reveals a wide gulf between the concepts as perceived to be taught and as actually learned by the students

Bi-layer splitting in overdoped high TcT_{c} cuprates

Recent angle-resolved photoemission data for overdoped Bi2212 are explained. Of the peak-dip-hump structure, the peak corresponds the $\vec q =0$ component of a hole condensate which appears at $T_c$. The fluctuating part of this same condensate produces the hump. The bilayer splitting is large enough to produce a bonding hole and an electron antibonding quasiparticle Fermi surface. Smaller bilayer splittings observed in some experiments reflect the interaction of the peak structure with quasiparticle states near, but not at, the Fermi surface.Comment: 4 pages with 2 figures - published versio

The Factory and The Beehive I. Rotation Periods For Low-Mass Stars in Praesepe

Stellar rotation periods measured from single-age populations are critical for investigating how stellar angular momentum content evolves over time, how that evolution depends on mass, and how rotation influences the stellar dynamo and the magnetically heated chromosphere and corona. We report rotation periods for 40 late-K to mid-M stars members of the nearby, rich, intermediate-age (~600 Myr) open cluster Praesepe. These rotation periods were derived from ~200 observations taken by the Palomar Transient Factory of four cluster fields from 2010 February to May. Our measurements indicate that Praesepe's mass-period relation transitions from a well-defined singular relation to a more scattered distribution of both fast and slow rotators at ~0.6 Msun. The location of this transition is broadly consistent with expectations based on observations of younger clusters and the assumption that stellar-spin down is the dominant mechanism influencing angular momentum evolution at 600 Myr. However, a comparison to data recently published for the Hyades, assumed to be coeval to Praesepe, indicates that the divergence from a singular mass-period relation occurs at different characteristic masses, strengthening the finding that Praesepe is the younger of the two clusters. We also use previously published relations describing the evolution of rotation periods as a function of color and mass to evolve the sample of Praesepe periods in time. Comparing the resulting predictions to periods measured in M35 and NGC 2516 (~150 Myr) and for kinematically selected young and old field star populations suggests that stellar spin-down may progress more slowly than described by these relations.Comment: To appear in the ApJ. 18 pages, 12 figures; version with higher resolution figures available at http://www.astro.columbia.edu/~marcel/papers/praesepe.pdf. Paper title inspired by local news; see http://tinyurl.com/redhone

Dynamics of spin ladders

We derive an approximate theory for Heisenberg spin ladders with two legs by mapping the spin dynamics onto the problem of hard-core `bond-Bosons'. The parameters of the Bosonic Hamiltonian are obtained by matching anomalous Green's functions to Lanczos results and we find evidence for a strong renormalization due to quantum fluctuations. Various dynamical spin correlation functions are calculated and found to be in good agreement with Lanczos results. We then enlarge the effective Hamiltonian to describe the coupling of the bond-Bosons to a single hole injected into the system and treat the hole-dynamics within the `rainbow-diagram' approximation by Schmidt-Rink et. al. Theoretical predictions for the single hole spectral function are obtained and found to be in good agreement with Lanczos results.Comment: RevTex-file, 10 PRB pages with 7 eps files. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to: [email protected]

Short-range repulsion and isospin dependence in the KN system

The short-range properties of the KN interaction are studied within the meson-exchange model of the Juelich group. Specifically, dynamical explanations for the phenomenological short-range repulsion, required in this model for achieving agreement with the empirical KN data, are explored. Evidence is found that contributions from the exchange of a heavy scalar-isovector meson (a_0(980)) as well as from genuine quark-gluon exchange processes are needed. Taking both mechanisms into account a satisfactory description of the KN phase shifts can be obtained without resorting to phenomenological pieces.Comment: 26 pages, 5 figure