Cosmology of a Friedmann-Lama\^itre-Robertson-Walker 3-brane, Late-Time Cosmic Acceleration, and the Cosmic Coincidence

A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence -- the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction. In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lama\^itre-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti-de Sitter spacetime. We derive the four-dimensional effective action on a FLRW 3-brane, which helps define a general reduction formula, namely, $M_P^{2}=\rho_{b}/|\Lambda_5|$, where $M_{P}$ is the effective Planck mass, $\Lambda_5$ is the 5-dimensional cosmological constant, and $\rho_b$ is the sum of the 3-brane tension $V$ and the matter density $\rho$. The behavior of the background solution is consistent with the results based on the form of the 4D effective potential. Although the range of variation in $\rho_{b}$ is strongly constrained, the big bang nucleosynthesis bound on the time variation of the renormalized Newton constant $G_N = (8\pi M_P^2)^{-1}$ is satisfied when the ratio $V/\rho \gtrsim {O} (10^2)$ on cosmological scales. The same bound leads to an effective equation of state close to -1 at late epochs in accordance with current astrophysical and cosmological observations.Comment: 5 pages, 3 figures; v2: version to be published in PR

On the feasibility of real-time prediction of aircraft carrier motion at sea

The ability to predict the aircraft carrier's motion over an interval of several seconds within reasonable error bounds may allow an improvement in touchdown dispersion and a more certain value for ramp clearance due to a smoother aircraft trajectory. Also, improved information to the landing signal officer should decrease the number of waveoffs substantially. It is quantitatively shown that, based on the power density spectrum data for pitch and heave measured for various ships and sea conditions, the motion can be predicted well for up to 15 seconds. The zero crossover times for both pitch and heave motions can be predicted with impressive accuracy. The predictor was designed on the basis of Kalman's optimum filtering theory for the discrete time case, adapted for real-time digital computer operation

Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control

Approaching the Standard Quantum Limit of Mechanical Torque Sensing

Mechanical transduction of torque has been key to probing a number of physical phenomena, such as gravity, the angular momentum of light, the Casimir effect, magnetism, and quantum oscillations. Following similar trends as mass and force sensing, mechanical torque sensitivity can be dramatically improved by scaling down the physical dimensions, and therefore moment of inertia, of a torsional spring. Yet now, through precision nanofabrication and sub-wavelength cavity optomechanics, we have reached a point where geometric optimization can only provide marginal improvements to torque sensitivity. Instead, nanoscale optomechanical measurements of torque are overwhelmingly hindered by thermal noise. Here we present cryogenic measurements of a cavity-optomechanical torsional resonator cooled in a dilution refrigerator to a temperature of 25 mK, corresponding to an average phonon occupation of = 35, that demonstrate a record-breaking torque sensitivity of 2.9 yNm/Hz^{1/2}. This a 270-fold improvement over previous optomechanical torque sensors and just over an order of magnitude from its standard quantum limit. Furthermore, we demonstrate that mesoscopic test samples, such as micron-scale superconducting disks, can be integrated with our cryogenic optomechanical torque sensing platform, in contrast to other cryogenic optomechanical devices, opening the door for mechanical torque spectroscopy of intrinsically quantum systems.Comment: 25 pages, 7 figure

Exploring qualitative comparative analysis in IS Research

Qualitative Comparative Analysis (QCA) has been proposed as a promising qualitative data analysis strategy to study complex problems. QCA provides multiple conjunctural causation that can address generalizability concerns associated with case study research within the IS and other social science disciplines. However, there are not many studies that offer guidelines on how to effectively apply this methodology to IS research. This paper outlines a set of methodological principles for using QCA. An illustrative example of case studies of collaborative networks is discussed to demonstrate the application of QCA

An analog computer study of the effectiveness of interceptor commands derived from a prediction equation of second order

Analog computer study of effectiveness of interceptor commands derived from prediction equation of second orde