Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

Anisotropy induced in a silver-chloride emulsion by two incoherent and perpendicular light vibrations

After a report on the composition of two incoherent rectilinear vibrations with perpendicular polarizations, we suggest in this paper a method of extraction of the difference between two images in incoherent and polarized light. The images, perpendicularly polarized, are simultaneously recorded on a silver chloride emulsion H where an optical anisotropy is induced only in the areas where the incident intensity distributions are not identical. After exposure, H, observed between crossed polarizers, displays the difference between the two original images in its image plane. In addition, it is shown that the sign of this difference is retrieved by means of the dichroism of the plate.     

The kinetic boundary layer for the Klein-Kramers equation; A new numerical approach

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.     

Impact of interstitial air holes on a wide-bandwidth rejection filter made from a photonic crystal fiber

We have investigated the spectral properties of a band rejection filter made with a long-period fiber grating written in photonic crystal fiber that has interstitial air holes. Experiments showed that only one mode was coupled strongly to the fundamental core mode over a 600 nm spectral range. The central wavelength of the filter could be tuned over that range without being appreciably affected by any other mode. By using the multipole method, we found that the interstitial air holes of the photonic crystal fiber played a critical role in limiting the number of modes that could strongly interact with the fundamental mode and in obtaining well-separated resonance peaks. Excellent agreement between theory and experiment was obtained.     

Deuterium dilution technique for body composition assessment: resolving methodological issues in children with moderate acute malnutrition

Childhood malnutrition is highly prevalent and associated with high mortality risk. In observational and interventional studies among malnourished children, body composition is increasingly recognised as a key outcome. The deuterium dilution technique has generated high-quality data on body composition in studies of infants and young children in several settings, but its feasibility and accuracy in children suffering from moderate acute malnutrition requires further study. Prior to a large nutritional intervention trial among children with moderate acute malnutrition, we conducted pilot work to develop and adapt the deuterium dilution technique. We refined procedures for administration of isotope doses and collection of saliva. Furthermore, we established that equilibration time in local context is 3?h. These findings and the resulting standard operating procedures are important to improve data quality when using the deuterium dilution technique in malnutrition studies in field conditions, and may encourage a wider use of isotope techniques.     

Bohr-sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula

We show how the moduli space of flatSU(2) connections on a two-manifold can be quantized in the real polarization of [15], using the methods of [6]. The dimension of the quantization, given by the number of integral fibres of the polarization, matches the Verlinde formula, which is known to give the dimension of the quantization of this space in a Kähler polarization.Supported in part by MSRI under NSF Grant 85-05550Supported in part by an NSF Graduate fellowship, and by a grant-in-aid from the J. Seward Johnson Charitable TrustSupported in part by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291. Address as of January 1, 1993: Department of Mathematics, Columbia University, New York, NY 10027, USA     

Emission spectrum of hot HDO below 4000 cm

Fourier transform emission spectra were recorded using a mixture of H₂O and D₂O at a temperature of 1500 °C. The spectra were recorded in three overlapping sections and cover the wavenumber range 1800-3932 cm⁻¹. This spectrum is analyzed together with a previously reported one spanning the 380-2190 cm⁻¹ range [Parekunnel et al., J. Mol. Spectrosc. 2001 (28) 101]. This analysis leads to 4409 newly assigned HDO emission lines. This work particularly extends data on the (200) and (120) states of HDO for which newly determined energy levels are presented.     

Spectroscopically determined potential energy surfaces of the H2O, H2O, and H2O isotopologues of water

Adiabatic potential energy surfaces (PESs) for three major isotopologues of water, H₂¹⁶O, H₂¹⁷O, and H₂¹⁸O, are constructed by fitting to observed vibration-rotation energy levels of the system using the nuclear motion program DVR3D employing an exact kinetic energy operator. Extensive tests show that the mass-dependent ab initio surfaces due to Polyansky et al. [O.L. Polyansky, A.G. Császár, S.V. Shirin, N.F. Zobov, P. Barletta, J. Tennyson, D.W. Schwenke, P.J. Knowles, Science 299 (2003) 539-542.] provide an excellent starting point for the fits. The refinements are performed using a mass-independent morphing function, which smoothly distorts the original adiabatic ab initio PESs. The best overall fit is based on 1788 experimental energy levels with the rotational quantum number J = 0, 2, and 5. It reproduces these levels with a standard deviation of 0.079 cm⁻¹ and gives, when explicit allowance is made for nonadiabatic rotational effects, excellent predictions for levels up to J = 40. Theoretical linelists for all three isotopologues of water involved in the PES construction were calculated up to 26 000 cm⁻¹ with energy levels up to J = 10. These linelists should make an excellent starting point for spectroscopic modelling and analysis.