Scaling of the Thue-Morse diffraction measure

We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained

Evaporation and Discharge Dynamics of Highly Charged Multicomponent Droplets Generated by Electrospray Ionization

We investigate the Rayleigh discharge and evaporation dynamics of highly charged two-component droplets consisting principally of methanol with 2-methoxyethanol, tert-butanol, or m-nitrobenzyl alcohol. A phase Doppler anemometer (PDA) characterizes droplets generated by electrospray ionization (ESI) according to size, velocity, and charge as they move through a uniform electric field within an ion mobility spectrometer (IMS). Repeated field reversals result in droplet “ping-pong” through the PDA. This generates individual droplet histories of solvent evaporation behavior and the dynamics of charge loss to progeny droplets during Rayleigh discharge events. On average, methanol droplets discharge at 127% their Rayleigh limit of charge, q_R, and release 25% of the net charge. Charge loss from methanol/2-methoxyethanol droplets behaves similarly to pure 2-methoxyethanol droplets which release ~28% of their net charge. Binary methanol droplets containing up to 50% tert-butanol discharge at a lower percent q_R than pure methanol and release a greater fraction of their net charge. Mixed 99% methanol/1% m-nitrobenzyl alcohol droplets possess discharge characteristics similar to those of methanol. However, droplets of methanol containing 2% m-nitrobenzyl evaporate down to a fixed size and charge that remains constant with no observable discharges. Quasi-steady-state evaporation models accurately describe observed evaporation phenomena in which methanol/tert-butanol droplets evaporate at a rate similar to that of pure methanol and methanol/2-methoxyethanol droplets evaporate at a rate similar to that of 2-methoxyethanol. We compare these results to previous Rayleigh discharge experiments and discuss the implications for binary solvents in electrospray mass spectrometry (ESI-MS) and field-induced droplet ionization mass spectrometry (FIDI-MS)

Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space H-2 that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided

Statistical properties of the combined emission of a population of discrete sources: astrophysical implications

We study the statistical properties of the combined emission of a population of discrete sources (e.g. X-ray emission of a galaxy due to its X-ray binaries population). Namely, we consider the dependence of their total luminosity L_tot=SUM(L_k) and of fractional rms_tot of their variability on the number of sources N or, equivalently, on the normalization of the luminosity function. We show that due to small number statistics a regime exists, in which L_tot grows non-linearly with N, in an apparent contradiction with the seemingly obvious prediction =integral(dN/dL*L*dL) ~ N. In this non-linear regime, the rms_tot decreases with N significantly more slowly than expected from the rms ~ 1/sqrt(N) averaging law. For example, for a power law luminosity function with a slope of a=3/2, in the non-linear regime, L_tot ~ N^2 and the rms_tot does not depend at all on the number of sources N. Only in the limit of N>>1 do these quantities behave as intuitively expected, L_tot ~ N and rms_tot ~ 1/sqrt(N). We give exact solutions and derive convenient analytical approximations for L_tot and rms_tot. Using the total X-ray luminosity of a galaxy due to its X-ray binary population as an example, we show that the Lx-SFR and Lx-M* relations predicted from the respective ``universal'' luminosity functions of high and low mass X-ray binaries are in a good agreement with observations. Although caused by small number statistics the non-linear regime in these examples extends as far as SFR<4-5 Msun/yr and log(M*/Msun)<10.0-10.5, respectively.Comment: MNRAS, accepted for publicatio

Lx-SFR relation in star forming galaxies

We compare the results of Grimm et al. (2003) and Ranalli et al. (2003) on the Lx-SFR relation in normal galaxies. Based on the Lx-stellar mass dependence for LMXBs, we show, that low SFR (SFR<1 Msun/year) galaxies in the Ranalli et al. sample are contaminated by the X-ray emission from low mass X-ray binaries, unrelated to the current star formation activity. The most important conclusion from our comparison is, however, that after the data are corrected for the ``LMXB contamination'', the two datasets become consistent with each other, despite of their different content, variability effects, difference in the adopted source distances, X-ray flux and star formation rate determination and in the cosmological parameters used in interpreting the HDF-N data. They also agree well, both in the low and high SFR regimes, with the predicted Lx-SFR dependence derived from the parameters of the ``universal'' HMXB luminosity function. This encouraging result emphasizes the potential of the X-ray luminosity as an independent star formation rate indicator for normal galaxies.Comment: revised, accepted for publication in MNRAS Letter

A critical Ising model on the Labyrinth

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.Comment: 25 pages, 6 figure

Hot-spot tectonics of Eistla Regio, Venus: Results from Magellan images and Pioneer Venus gravity

Eistla Regio (ER) is a broad, low, discontinuous topographic rise striking roughly EW at low northern latitudes of Venus. Some 2000 x 7000 km in dimensions, it is the third largest rise in planform on Venus after Aphrodite Terra and Beta Phoebe Regiones. These rises are the key physiographic elements in a hot spot model of global tectonics including transient plume behavior. Since ER is the first such rise viewed by Magellan and the latitude is very favorable for Pioneer Venus gravity studies, some of the predictions of a time dependent hot spot model are tested. Western ER is defined as the rise including Gula and Sif Mons and central ER as that including Sappho Patera. Superior conjunction prevented Magellan from returning data on eastern ER (Pavlova) during the first mapping cycle. It is concluded that the western and central portions of ER, while part of the same broad topographic rise and tectonic framework, have distinctly different surface ages and gravity signatures. The western rise, including Gula and Sif Mons, is the expression of deep seated uplift with volcanism limited to the individual large shields. The eastern portion has been widely resurfaced more recently by thermal anomalies in the mantle

Virtuous Insightfulness

Insight often strikes us blind; when we aren’t expecting it, we suddenly see a connection that previously eluded us—a kind of ‘Aha!’ experience. People with a propensity to such experiences are regarded as insightful, and insightfulness is a paradigmatic intellectual virtue. What’s not clear, however, is just what it is in virtue of which being such that these experiences tend to happen to one renders one intellectually virtuous. This paper draws from both virtue epistemology as well as empirical work on the psychology of problem solving and creativity to make some inroads in accounting for insightfulness as an intellectual virtue. Important to the view advanced is that virtuously insightful individuals manifest certain skills which both cultivate insight experiences (even if not by directly bringing them about) and enable such individuals to move in an epistemically responsible way from insight experience to epistemic endorsement

On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups

We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a 'flavor' U(1)-gauge group.Comment: 33 pages, 4 figure