Showing papers by "Swaroop Darbha published in 2010"

Electromagnetic counterparts of compact object mergers powered by the radioactive decay of r‐process nuclei

Abstract: The most promising astrophysical sources of kHz gravitational waves (GWs) are the inspiral and merger of binary neutron star(NS)/black hole systems. Maximizing the scientific return of a GW detection will require identifying a coincident electromagnetic (EM) counterpart. One of the most likely sources of isotropic EM emission from compact object mergers is a supernova-like transient powered by the radioactive decay of heavy elements synthesized in ejecta from the merger. We present the first calculations of the optical transients from compact object mergers that self-consistently determine the radioactive heating by means of a nuclear reaction network; using this heating rate, we model the light curve with a one-dimensional Monte Carlo radiation transfer calculation. For an ejecta mass ~ 10 -2 M ⊙ (10 -3 M ⊙ ) the resulting light-curve peaks on a time-scale ~1 d at a V-band luminosity vL v ~ 3 x 10 41 (10 41 )erg s -1 [M V = -15(-14)]; this corresponds to an effective 'f' parameter ~3 × 10- 6 in the Li-Paczynski toy model. We argue that these results are relatively insensitive to uncertainties in the relevant nuclear physics and to the precise early-time dynamics and ejecta composition. Since NS merger transients peak at a luminosity that is a factor of ~10 3 higher than a typical nova, we propose naming these events 'kilo-novae'. Because of the rapid evolution and low luminosity of NS merger transients, EM counterpart searches triggered by GW detections will require close collaboration between the GW and astronomical communities. NS merger transients may also be detectable following a short-duration gamma-ray burst or 'blindly' with present or upcoming optical transient surveys. Because the emission produced by NS merger ejecta is powered by the formation of rare r-process elements, current optical transient surveys can directly constrain the unknown origin of the heaviest elements in the Universe.

Today's Traveling Salesman Problem

Abstract: Heterogeneous unmanned aerial vehicles (UAVs) are being developed for several civil and military applications. These vehicles can differ either in their motion constraints or sensing/attack capabilities. This article uses methods from operations research to address a fundamental routing problem involving heterogeneous UAVs. The approach is to transform the routing problem into a relatively better understood single, asymmetric, traveling salesman problem (ATSP) and use the algorithms available for the ATSP to address the routing problem. To test the effectiveness of the transformation, the well-known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results on the transformed ATSP show that solutions whose costs are within 16% of the optimum can be obtained relatively fast [within 40 s of central processing unit (CPU)] for the routing problem involving ten heterogeneous UAVs and 40 targets.

Nickel-rich outflows produced by the accretion-induced collapse of white dwarfs: light curves and spectra

Abstract: The accretion-induced collapse (AIC) of a white dwarf to form a neutron star can leave behind a rotationally supported disc with mass of up to ~0.1 M ⊙ . The disc is initially composed of free nucleons but as it accretes and spreads to larger radii, the free nucleons recombine to form helium, releasing sufficient energy to unbind the remaining disc. Most of the ejected mass fuses to form 56 Ni and other iron group elements. We present spherically symmetric radiative transfer calculations of the transient powered by the radioactive heating of this ejecta. We estimate the ejecta composition using nucleosynthesis calculations in the literature and explore the sensitivity of our results to uncertainties in the ejecta kinematics. For an ejecta mass of 10 -2 M ⊙ (3 × 10 -3 M ⊙ , the light curve peaks after ≲1 d with a peak bolometric luminosity ≃2 x 10 41 erg s -1 (≃5 x 10 40 erg s -1 ); the decay time is ≃4(2) d. Overall, the spectra redden with time reaching U - V ≃ 4 after ≃1 d; the optical colours (B- V) are, however, somewhat blue. Near the peak in the light curve, the spectra are dominated by Doppler-broadened Nickel features, with no distinct spectral lines present. At ~3-5 d, strong calcium lines are present in the infrared, although the calcium mass fraction is only ~10 -4.5 . If rotationally supported discs are a common byproduct of AIC, current and upcoming transient surveys such as the Palomar Transient Factory should detect a few AIC per year for an AIC rate of ~10 -2 of the Type Ia rate. We discuss ways of distinguishing AIC from other rapid, faint transients, including .Ia's and the ejecta from binary neutron star mergers.

Sampling-Based Roadmap Methods for a Visual Reconnaissance UAV ∗

Abstract: This article considers a path planning problem for a single fixed-wing aircraft performing a reconnaissance mission using EO (Electro-Optical) camera(s). A mathematical formulation of the general aircraft visual reconnaissance problem for static ground targets in terrain is given and it is shown, under simplifying assumptions, that it can be reduced to what we call the PVDTSP (Polygon-Visiting Dubins Traveling Salesman Problem), a variation of the famous TSP (Traveling Salesman Problem). Two algorithms are developed to solve the PVDTSP. They fall into the class of algorithms known as sampling-based roadmap methods because they operate by sampling a finite set of points from a continuous state space in order to reduce a continuous motion planning problem to planning on a finite discrete graph. The first method is resolution complete, which means it provably converges to a nonisolated global optimum as the number of samples grows. The second method achieves slightly shorter computation times by using approximate dynamic programming, but consequently is only guaranteed to converge to a nonisolated global optimum modulo target order. Numerical experiments indicate that, for up to about 20 targets, both methods deliver good solutions suitably quickly for online purposes. Additionally, both algorithms allow trade-off of computation time for solution quality and are shown extensible to handle wind, airspace constraints, any vehicle dynamics, and open-path (vs. closed-tour) problems.

State aggregation based linear programming approach to approximate dynamic programming

Abstract: One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound for the deviation of such a policy from the optimum through the use of restricted linear programming. The novelty of this approach lies in circumventing the need for a value iteration or a linear program defined on the entire state-space. Instead, the state-space is partitioned based on the reward structure and the optimal cost-to-go or value function is approximated by a constant over each partition. We associate a meta-state with each partition, where the transition probabilities between these meta-states can be derived from the original Markov chain specification. The state aggregation approach results in a significant reduction in the computational burden and lends itself to a restricted linear program defined on the aggregated state-space. Finally, the proposed method is bench marked on a perimeter surveillance stochastic control problem.

On the vibrations of lumped parameter systems governed by differential-algebraic equations

Abstract: In this paper, we consider the vibratory motions of lumped parameter systems wherein the components of the system cannot be described by constitutive expressions for the force in terms of appropriate kinematical quantities. Such physical systems reduce to a system of differential-algebraic equations, which invariably need to be solved numerically. To illustrate the issues with clarity, we consider a simple system in which the dashpot is assumed to contain a “Bingham” fluid for which one cannot describe the force in the dashpot as a function of the velocity. On the other hand, one can express the velocity as a function of the force.