Horizon fluxes of binary black holes in eccentric orbits

I compute the rate of change of mass and angular momentum of a black hole, namely tidal heating, in an eccentric orbit. The change is caused due to the tidal field of the orbiting companion. I compute the result for both the spinning and non-spinning black holes in the leading order of the mean motion, namely $\xi$. I demonstrate that the rates get enhanced significantly for nonzero eccentricity. Since eccentricity in a binary evolves with time I also express the results in terms of an initial eccentricity and azimuthal frequency $\xi_{\phi}$. In the process, I developed a prescription that can be used to compute all physical quantities in a series expansion of initial eccentricity, $e_0$. This result was only known in the leading order while ignoring the contribution of the spin on the eccentricity evolution. Although the eccentricity evolution result still ignores the spin effect in the current work, the prescription can be used to compute higher-order corrections of initial eccentricity post-leading order. Using this result I computed the rate of change of mass and angular momentum of a black hole in terms of initial eccentricity and azimuthal frequency up to $\mathcal{O}(e_0^2)$.Comment: arXiv admin note: text overlap with arXiv:1605.00304 by other author

On the Consistency of Maximum Likelihood Estimation of Probabilistic Principal Component Analysis

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of applications ranging from science and engineering to quantitative finance. Despite this wide applicability in various fields, hardly any theoretical guarantees exist to justify the soundness of the maximal likelihood (ML) solution for this model. In fact, it is well known that the maximum likelihood estimation (MLE) can only recover the true model parameters up to a rotation. The main obstruction is posed by the inherent identifiability nature of the PPCA model resulting from the rotational symmetry of the parameterization. To resolve this ambiguity, we propose a novel approach using quotient topological spaces and in particular, we show that the maximum likelihood solution is consistent in an appropriate quotient Euclidean space. Furthermore, our consistency results encompass a more general class of estimators beyond the MLE. Strong consistency of the ML estimate and consequently strong covariance estimation of the PPCA model have also been established under a compactness assumption.Comment: 15 pages, 1 figure, to appear in NeurIPS 2023. Update: included minor typographical correction

Relativistic tidal properties of superfluid neutron stars

We investigate the tidal deformability of a superfluid neutron star. We calculate the equilibrium structure in the general relativistic two-fluid formalism with entrainment effect where we take neutron superfluid as one fluid and the other fluid is comprised of protons and electrons, making it a charge neutral fluid. We use a relativistic mean field model for the equation of state of matter where the interaction between baryons is mediated by the exchange $\sigma$, $\omega$ and $\rho$ mesons. Then, we study the linear, static $l=2$ perturbation on the star to compute the electric-type Love number following Hinderer's prescription.Comment: Accepted for publication in Physical Review

Imprint of black hole area quantization and Hawking radiation on inspiraling binary

We study the potential of gravitational wave astronomy to observe the quantum aspects of black holes. According to Bekenstein's quantization, we find that black hole area discretization can have observable imprints on the gravitational wave signal from an inspiraling binary black hole. We study the impact of quantization on tidal heating. We model the absorption lines and compute gravitational wave flux due to tidal heating in such a case. By including the quantization we find the dephasing of the gravitational wave, to our knowledge it has never been done before. We discuss the observability of the phenomena in different parameter ranges of the binary. We show that in the inspiral, it leads to vanishing tidal heating for the high spin values. Therefore measuring non-zero tidal heating can rule out area quantization. We also argue that if area quantization is present in nature then our current modeling with reflectivity can possibly probe the Hawking radiation which may bring important information regarding the quantum nature of gravity

Synthesis of gold nano-particles in a microfluidic platform for water quality monitoring applications

A microfluidic lab-on-a-chip (LOC) device for in-situ synthesis of gold nano-particles was developed. The long term goal is to develop a portable hand-held diagnostic platform for monitoring water quality (e.g., detecting metal ion pollutants). The LOC consists of micro-chambers housing different reagents and samples that feed to a common reaction chamber. The reaction products are delivered to several waste chambers in a pre-defined sequence to enable reagents/ samples to flow into and out of the reaction chamber. Passive flow actuation is obtained by capillary driven flow (wicking) and dissolvable microstructures called ‘salt pillars’. The LOC does not require any external power source for actuation and the passive microvalves enable flow actuation at predefined intervals. The LOC and the dissolvable microstructures are fabricated using a combination of photolithography and soft lithography techniques. Experiments were conducted to demonstrate the variation in the valve actuation time with respect to valve position and geometric parameters. Subsequently, analytical models were developed using one dimensional linear diffusion theory. The analytical models were in good agreement with the experimental data. The microvalves were developed using various salts: polyethylene glycol, sodium chloride and sodium acetate. Synthesized in-situ in our experiments, gold nano-particles exhibit specific colorimetric and optical properties due to the surface plasmon resonance effect. These stabilized mono-disperse gold nano-particles can be coated with bio-molecular recognition motifs on their surfaces. A colorimetric peptide assay was thus developed using the intrinsic property of noble metal nano-particles. The LOC device was further developed on a paper microfluidics platform. This platform was tested successfully for synthesis of gold nano-particles using a peptide assay and using passive salt-bridge microvalves. This study proves the feasibility of a LOC device that utilizes peptide assay for synthesis of gold nano-particles in-situ. It could be highly significant in a simple portable water quality monitoring platform