Hyperbolic/parabolic development for the GIM-STAR code

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated

Development of the general interpolants method for the CYBER 200 series of supercomputers

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included

AC Stark shift noise in QND measurement arising from quantum fluctuations of light polarization

In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization.Comment: This is a companion note to physics/040309

Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?

Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. Fundamental noise sources include the quantum projection noise and the photon shot-noise. For measurement times much shorter than the spin-relaxation time observed in the absence of light ($\tau_{\rm rel}$) divided by $\sqrt{N}$, the optimal sensitivity of the magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity scaling as $N^{-1/2}$ can be achieved. However, at longer measurement times, the optimized sensitivity scales as $N^{-1/2}$, as for a usual shot-noise limited magnetometer. If strongly squeezed probe light is used, the Heisenberg uncertainty limit may, in principle, be reached for very short measurement times. However, if the measurement time exceeds $\tau_{\rm rel}/N$, the $N^{-1/2}$ scaling is again restored.Comment: Some details of calculations can be found in a companion note: physics/040712

Velocity-selective direct frequency-comb spectroscopy of atomic vapors

We present an experimental and theoretical investigation of two-photon direct frequency-comb spectroscopy performed through velocity-selective excitation. In particular, we explore the effect of repetition rate on the $\textrm{5S}_{1/2}\rightarrow \textrm{5D}_{3/2, 5/2}$ two-photon transitions excited in a rubidium atomic vapor cell. The transitions occur via step-wise excitation through the $\textrm{5P}_{1/2, 3/2}$ states by use of the direct output of an optical frequency comb. Experiments were performed with two different frequency combs, one with a repetition rate of $\approx 925$ MHz and one with a repetition rate of $\approx 250$ MHz. The experimental spectra are compared to each other and to a theoretical model.Comment: 10 pages, 7 figure

The Relationship Between Belief and Credence

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the debate thus far

Realism, Objectivity, and Evaluation

I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are widely identified, are actually in tension

Against Motivational Efficacy of Beliefs

Bromwich (2010) argues that a belief is motivationally efficacious in that, other things being equal, it disposes an agent to answer a question in accordance with that belief. I reply that what we are disposed to do is largely determined by our genes, whereas what we believe is largely determined by stimuli from the environment. We have a standing and default disposition to answer questions honestly, ceteris paribus, even before we are exposed to environmental stimuli. Since this standing and default disposition is innate, and our beliefs have their source in environmental stimuli, our beliefs cannot be the source of the disposition. Moreover, a recent finding in neuroscience suggests that motivation is extrinsic to belief

Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documente