Pre-Merger Localization of Gravitational-Wave Standard Sirens With LISA I: Harmonic Mode Decomposition

The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole (SMBH) binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to SMBH binary mergers with total mass M~10^5-10^7 M_Sun and redshifts z<~3 can be localized to within the field of view of astronomical instruments (~deg^2) typically hours to weeks prior to coalescence. This will allow targeted searches for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.Comment: 29 pages, 12 figures, version accepted by Phys Rev

Static QˉQ\bar{Q}Q pair free energy and screening masses from correlators of Polyakov loops: continuum extrapolated lattice results at the QCD physical point

We study the correlators of Polyakov loops, and the corresponding gauge invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at finite temperature. Our simulations were carried out on $N_t$ = 6, 8, 10, 12, 16 lattices using Symanzik improved gauge action and a stout improved staggered action with physical quark masses. The free energies calculated from the Polyakov loop correlators are extrapolated to the continuum limit. For the free energies we use a two step renormalization procedure that only uses data at finite temperature. We also measure correlators with definite Euclidean time reversal and charge conjugation symmetry to extract two different screening masses, one in the magnetic, and one in the electric sector, to distinguish two different correlation lengths in the full Polyakov loop correlator

Typical Borel measures on [0,1]d[0,1]d satisfy a multifractal formalism

In this article, we prove that in the Baire category sense, measures supported by the unit cube of $\R^d$ typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures $\mu$. This spectrum appears to be linear with slope 1, starting from 0 at exponent 0, ending at dimension $d$ at exponent $d$, and it indeed coincides with the Legendre transform of the $L^q$-spectrum associated with typical measures $\mu$.Comment: 17 pages. To appear in Nonlinearit

Evaluation of the Loss of Uniaxial Compressive Strength of Sandstones Due to Moisture

The reduction in uniaxial compressive strength (UCS) was investigated for sandstones under various moisture levels. Thirty-four UK Darney sandstone samples were tested under six different moisture conditions. The time-dependent moisture gain and loss were also evaluated. For 77 sandstones identified in the literature, the loss of UCS between oven-dry and saturated conditions was up to 45%, with an average of 20%. For Darney stone, the average loss of UCS was around 20%, with UCS around 72 N/mm2 when oven-dry and 58 N/mm2 when fully saturated. During saturation, significant loss of UCS occurred soon after exposure to water with 80% of UCS being lost within the first 2.5–6 hours. For Darney stone 50% of UCS was lost at air-dry conditions. Results from the 78 sandstone types were compared with the equivalent compressive strength defined by BS EN 772–1:2011 for oven-dry, air-dry, and saturated conditions. The estimated values by BS EN 772–1:2011 for dry and saturated UCS agreed well with the available test data and indicated a lower-bound solution. For immersed conditions, BS EN 772–1:2011, however, overestimates the reduction in UCS for a large number of samples and provides an average, instead of a lower-bound solution

Four-jet angular distributions and color charge measurements: leading order versus next-to-leading order

We present the next-to-leading order perturbative QCD prediction to the four-jet angular distributions used by experimental collaborations at LEP for measuring the QCD color charge factors. We compare our results to ALEPH data corrected to parton level. We perform a leading order ``measurement'' of the QCD color factor ratios by fitting the leading order perturbative predictions to the next-to-leading order result. Our result shows that in an experimental analysis for measuring the color charge factors the use of the O($\alpha_s^3$) QCD predictions instead of the O($\alpha_s^2$) results may shift the center of the fit by a relative factor of 1+2\as in the $T_R/C_F$ direction.Comment: 14 pages, 10 tables, 5 figures, revtex, eps style