52,125 research outputs found
Verifying black hole orbits with gravitational spectroscopy
Gravitational waves from test masses bound to geodesic orbits of rotating
black holes are simulated, using Teukolsky's black hole perturbation formalism,
for about ten thousand generic orbital configurations. Each binary radiates
power exclusively in modes with frequencies that are
integer-linear-combinations of the orbit's three fundamental frequencies. The
following general spectral properties are found with a survey of orbits: (i)
99% of the radiated power is typically carried by a few hundred modes, and at
most by about a thousand modes, (ii) the dominant frequencies can be grouped
into a small number of families defined by fixing two of the three integer
frequency multipliers, and (iii) the specifics of these trends can be
qualitatively inferred from the geometry of the orbit under consideration.
Detections using triperiodic analytic templates modeled on these general
properties would constitute a verification of radiation from an adiabatic
sequence of black hole orbits and would recover the evolution of the
fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this
would compare to observing the Bohr model's atomic hydrogen spectrum without
being able to rule out alternative atomic theories or nuclei. The suitability
of such a detection technique is demonstrated using snapshots computed at
12-hour intervals throughout the last three years before merger of a kludged
inspiral. Because of circularization, the number of excited modes decreases as
the binary evolves. A hypothetical detection algorithm that tracks mode
families dominating the first 12 hours of the inspiral would capture 98% of the
total power over the remaining three years.Comment: 18 pages, expanded section on detection algorithms and made minor
edits. Final published versio
Interpreting markups in Spanish manufacturing: the exponential model
In this paper we attempt to rationalize markups in a sample of Spanish manufacturing by assuming a representative consumer, profit-maximizing firms and constant returns to scale. We find that the standard forms of demand (CES and linear) do not provide a good explanation of markups. In contrast, a model where the representative consumer has an exponential utilty function yields results that match data more closely.
Interpreting markups in Spanish manufacturing: The exponential model
In this paper we attempt to rationalize markups in a sample of Spanish manufacturing by assuming a representative consumer, profit-maximizing firms and constant returns to scale. We find that the standard forms of demand (CES and linear) do not provide a good explanation of markups. In contrast, a model where the representative consumer has an exponential utilty function yields results that match data more closely.Markups, Exponential utility function
The scholarship assignment problem
There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome.Publicad
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