Monte Carlo Integration with Subtraction

This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations; the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student's t-test as a trigger for rebinning, which we claim is more stable than the \chi-squared test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of one-dimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading.Comment: Code PANIC included as a set of ancillary file

Legal fee restrictions, moral hazard, and attorney profits

When attorney effort is unobservable and certain other simplifying assumptions (such as risk neutrality) hold, it is efficient for an attorney to purchase the rights to a client's legal claim. However, the American Bar Association Model Rules of Professional Conduct prohibit this arrangement. We show that this ethical restriction, which is formally equivalent to requiring a minimum fixed fee of zero, can create economic rents for attorneys, even though they continue to compete along the contingent-fee dimension. The contingent fee is not bid down to the zero-profit level, because such a fee does not induce sufficient attorney effort. We thereby provide a political economy explanation for these restrictions.

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000

Comments on the role of diagonal dominance in implicit difference methods

Numerical tests were made for a model of the Navier-Stokes equations using a second-order accurate implicit scheme which guarantees diagonal dominance. The results suggest that the failure of implicit methods using large marching steps may not always be attributed to the lack of diagonal dominance in the coefficient matrix. In some cases the failure may be caused by a nonlinear instability associated with the solution method

Preventing, Punishing and Eliminating Terrorism in the Western Hemisphere: A Post-9/11 Inter-American Treaty

Part I of this Article will provide a brief background to the fight against terrorism as seen from an inter-American legal and institutional standpoint. Part II will discuss the more significant details of the Convention and the negotiations in the Permanent Council\u27s Working Group that produced it. In II(A), the authors review the conflicting views among delegates about whether the OAS should have been negotiating a “comprehensive” anti-terrorism treaty (complete with a legal definition of terrorist acts) or follow the suggestion of the United States and adopt a less ambitious treaty providing some “added value” (by incorporating by reference the law-making of previous United Nations (“U.N.”) terrorism treaties). In II(B), the authors discuss treaty provisions dedicated to cooperation among hemispheric governments. In II(C), the Article explains treaty provisions on denying terrorists the benefits of asylum, refugee status, and the political offense exception in extradition law. In II(D), the treaty\u27s role as a supplement to other extradition treaties is noted. In II(E), the Article discusses what the treaty says about the money side of terrorism--what the hemisphere will do about tracking money, money laundering, and asset forfeiture. In II(F), the controversy over whether to mention human rights in the Convention is explained. In II(G), the authors discuss treaty provisions on permitting the transfer of prisoners among different countries in the Americas. In the Conclusion, the authors note that the American republics have taken a significant step forward in the codification of international law by negotiating a practical multilateral instrument

A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations

Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows

Mean flow field and surface heating produced by unequal shock interactions at hypersonic speeds

Mean velocity profiles were measured in a free shear layer produced by the interaction of two unequal strength shock waves at hypersonic free-stream Mach numbers. Measurements were made over a unit Reynolds number range of 3,770,000 per meter to 17,400,000 per meter based on the flow on the high velocity side of the shear layer. The variation in measured spreading parameters with Mach number for the fully developed flows is consistent with the trend of the available zero velocity ratio data when the Mach numbers for the data given in this study are taken to be characteristic Mach numbers based on the velocity difference across the mixing layer. Surface measurements in the shear-layer attachment region of the blunt-body model indicate peak local heating and static pressure consistent with other published data. Transition Reynolds numbers were found to be significantly lower than those found in previous data

Near-infrared Observations of Nova V574 Puppis (2004)

We present results obtained from extensive near-infrared spectroscopic and photometric observations of nova V574 Pup during its 2004 outburst. The observations were obtained over four months, starting from 2004 November 25 (four days after the nova outburst) to 2005 March 20. The near-IR JHK light curve is presented - no evidence is seen from it for dust formation to have occurred during our observations. In the early decline phase, the JHK spectra of the nova are dominated by emission lines of hydrogen Brackett and Paschen series, OI, CI and HeI. We also detect the fairly uncommon Fe II line at 1.6872 micron in the early part of our observations. The strengths of the HeI lines at 1.0830 micron and 2.0585 micron are found to become very strong towards the end of the observations indicating a progression towards higher excitation conditions in the nova ejecta. The width of the emission lines do not show any significant change during the course of our observations. The slope of the continuum spectrum was found to have a lambda^{-2.75} dependence in the early stages which gradually becomes flatter with time and changes to a free-free spectral dependence towards the later stages. Recombination analysis of the HI lines shows deviations from Case B conditions during the initial stages. However, towards the end of our observations, the line strengths are well simulated with case B model values with electron density n_e = 10^{9-10} cm^{-3} and a temperature equal to 10^4 K. Based on our distance estimate to the nova of 5.5 kpc and the observed free-free continuum emission in the later part of the observations, we estimate the ionized mass of the ejecta to be between 10^{-5} and 10^{-6} solar-mass.Comment: 10 pages, 8 figures, Accepted for publication in MNRA

Near-Infrared H and K band studies of the 2006 outburst of the recurrent nova RS Ophiuchi

We present near-IR photo-spectroscopy in the H and K bands of the 2006 outburst of the recurrent nova RS Ophiuchi (RS Oph). The observations cover the period between 1 to 94 days after the eruption. The near IR light curve and an extensive set of spectra are presented, lines identified and the general characteristics of the spectra discussed. Analysis of the HI line profiles show the presence of broad wings on both flanks of a strong central component indicating the presence of a bipolar velocity flow in the ejecta. Such a flow is kinematically consistent with the bipolar structure that the object displays in high-resolution spatial images. We discuss the behaviour and origin of the Fe II lines at 1.6872 and 1.7414 micron and show that Lyman alpha and Lyman continuum fluorescence are viable mechanisms to excite these lines. We draw upon the result, that collisional excitation can also contribute in exciting and significantly enhancing the strength of these Fe II lines, to propose that these lines originate from a site of high particle density. Such a likely site could be the high-density, low temperature contact surface that should exist in the shockfront in between the shocked ejecta and red giant wind. Recombination analysis of the HI lines indicate deviations from Case B conditions during most of the span of our observations indicating optical depth effects. It appears likely that the breakout of the shockfront had not yet occured till the end of our observations. An analysis is made of the temporal evolution of the [Si VI] 1.9641 micron coronal line and another coronal line at 2.0894 micron which is attributed to [Mn XIV]. Assuming collisional effects to dominate in the hot coronal gas, estimates are made of the ion temperature in the gas.Comment: Accepted in MNRAS. Accepted version with inclusion of additional analysi

Discovery of Two Simultaneous Kilohertz Quasi-Periodic Oscillations in KS 1731-260

We have discovered two simultaneous quasi-periodic oscillations (QPOs) at 898.3+/-3.3 Hz and 1158.6+/-9.0 Hz in the 1996 August 1 observation of the low-mass X-ray binary KS 1731-260 with the Rossi X-ray Timing Explorer. The rms amplitude and FWHM of the lower frequency QPO were 5.3+/-0.7 % and 22+/-8 Hz, whereas those of the higher frequency QPO were 5.2+/-1.0 % and 37+/-21 Hz. At low inferred mass accretion rate both QPOs are visible, at slightly higher mass accretion rate the lower frequency QPO disappears and the frequency of the higher frequency QPO increases to ~1178 Hz. At the highest inferred mass accretion rate this QPO is only marginally detectable (2.1 sigma) near 1207 Hz, which is the highest frequency so far observed in an X-ray binary. The frequency difference (260.3+/-9.6 Hz) between the QPOs is equal to half the frequency of the oscillations observed in a type I burst in this source (at 523.92+/-0.05 Hz, Smith, Morgan and Bradt 1997). This suggests that the neutron star spin frequency is 261.96 Hz (3.8 ms), and that the lower frequency QPO is the beat between the higher frequency QPO, which could be a preferred orbital frequency around the neutron star, and the neutron star spin. During the 1996 August 31 observation we detected an additional QPO at 26.9+/-2.3 Hz, with a FWHM and rms amplitude of 11+/-5 Hz and 3.4+/-0.6 %.Comment: 6 pages including 3 figures, Astrophysical Journal Letters, in press (issue 482