Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Rasim 10^9$. Power law scalings of $Nusim Ra^{gamma}$
are observed with $gammaapprox 0.31$, where the Nusselt number $Nu$ is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on $Pr$ is found to be extremely weak. On the other hand, the presence of two local maxima of $Nu$ with different horizontal wavenumbers at the same $Ra$ leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For $Pr lesssim 7$, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid which spawns left/right horizontal arms near the top of the channel, leading to downdrafts adjacent to the central updraft. For $Pr > 7$ at high-enough Ra, the optimal structure is a single updraft absent significant horizontal structure, and characterized by the larger maximal wavenumber.
Stackelberg security game models and associated computational tools have seen deployment in a number of high-consequence security settings, such as LAX canine patrols and Federal Air Marshal Service. These models focus on isolated systems with only o
ne defender, despite being part of a more complex system with multiple players. Furthermore, many real systems such as transportation networks and the power grid exhibit interdependencies between targets and, consequently, between decision makers jointly charged with protecting them. To understand such multidefender strategic interactions present in security, we investigate game theoretic models of security games with multiple defenders. Unlike most prior analysis, we focus on the situations in which each defender must protect multiple targets, so that even a single defenders best response decision is, in general, highly non-trivial. We start with an analytical investigation of multidefender security games with independent targets, offering an equilibrium and price-of-anarchy analysis of three models with increasing generality. In all models, we find that defenders have the incentive to over-protect targets, at times significantly. Additionally, in the simpler models, we find that the price of anarchy is unbounded, linearly increasing both in the number of defenders and the number of targets per defender. Considering interdependencies among targets, we develop a novel mixed-integer linear programming formulation to compute a defenders best response, and make use of this formulation in approximating Nash equilibria of the game. We apply this approach towards computational strategic analysis of several models of networks representing interdependencies, including real-world power networks. Our analysis shows how network structure and the probability of failure spread determine the propensity of defenders to over- or under-invest in security.
Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, th
e SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/nu-scaling of the inter-species radial transport coefficient at low collisionality, arising due to the field term in the inter-species collision operator, and which is not found with simplified collision models even when momentum correction is applied. However, this type of scaling disappears if a radial electric field is present. We also use SFINCS to analyze how the impurity content affects the neoclassical impurity dynamics and the bootstrap current. We show that a change in plasma effective charge Zeff of order unity can affect the bootstrap current enough to cause a deviation in the divertor strike point locations.
We develop a general framework for data analysis and phenomenology of the CMB four-point function or trispectrum. To lowest order in the derivative expansion, the inflationary action admits three quartic operators consistent with symmetry: $dotsigma^
4$, $dotsigma^2 (partialsigma^2)$, and $(partialsigma)^4$. In single field inflation, only the first of these operators can be the leading non-Gaussian signal. A Fisher matrix analysis shows that there is one near-degeneracy among the three CMB trispectra, so we parameterize the trispectrum with two coefficients $g_{NL}^{dotsigma^4}$ and $g_{NL}^{(partialsigma)^4}$, in addition to the coefficient $g_{NL}^{rm loc}$ of $zeta^3$-type local non-Gaussianity. This three-parameter space is analogous to the parameter space $(f_{NL}^{rm loc}, f_{NL}^{rm equil}, f_{NL}^{rm orth})$ commonly used to parameterize the CMB three-point function. We next turn to data analysis and show how to represent these trispectra in a factorizable form which leads to computationally fast operations such as evaluating a CMB estimator or simulating a non-Gaussian CMB. We discuss practical issues in CMB analysis pipelines, and perform an optimal analysis of WMAP data. Our minimum-variance estimates are $g_{NL}^{rm loc} = (-3.80 pm 2.19) times 10^5$, $g_{NL}^{dotsigma^4} = (-3.20 pm 3.09) times 10^6$, and $g_{NL}^{(partialsigma)^4} = (-10.8 pm 6.33) times 10^5$ after correcting for the effects of CMB lensing. No evidence of a nonzero inflationary four-point function is seen.
We present a measurement of the one-point probability distribution function (PDF) of the thermal Sunyaev-Zeldovich (tSZ) decrement in the pixel temperature histogram of filtered 148 GHz sky maps from the Atacama Cosmology Telescope (ACT). The PDF inc
ludes the signal from all galaxy clusters in the map, including objects below the signal-to-noise threshold for individual detection, making it a particularly sensitive probe of the amplitude of matter density perturbations, $sigma_8$. We use a combination of analytic halo model calculations and numerical simulations to compute the theoretical tSZ PDF and its covariance matrix, accounting for all noise sources and including relativistic corrections. From the measured ACT 148 GHz PDF alone, we find $sigma_8 = 0.793 pm 0.018$, with additional systematic errors of $pm 0.017$ due to uncertainty in intracluster medium gas physics and $pm 0.006$ due to uncertainty in infrared point source contamination. Using effectively the same data set, the statistical error here is a factor of two lower than that found in ACTs previous $sigma_8$ determination based solely on the skewness of the tSZ signal. In future temperature maps with higher sensitivity, the tSZ PDF will break the degeneracy between intracluster medium gas physics and cosmological parameters.
Using transient Rayleigh scattering (TRS) measurements, we obtain photoexcited carrier thermalization dynamics for both zincblende (ZB) and wurtzite (WZ) InP single nanowires (NW) with picosecond resolution. A phenomenological fitting model based on
direct band to band transition theory is developed to extract the electron-hole-plasma density and temperature as a function of time from TRS measurements of single nanowires which have complex valence band structures. We find that the thermalization dynamics of hot carriers depends strongly on material (GaAs NW vs. InP NW) and less strongly on crystal structure (ZB vs. WZ). The thermalization dynamics of ZB and WZ InP NWs are similar. But a comparison of the thermalization dynamics in ZB and WZ InP NWs with ZB GaAs NW reveals more than an order of magnitude slower relaxation for the InP NWs. We interpret these results as reflecting their distinctive phonon band structures which lead to different hot phonon effects. Knowledge of hot carrier thermalization dynamics is an essential component for effective incorporation of nanowire materials into electronic devices.
We present a characterization of short-term stability of random Boolean networks under emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides w
hether short-term chaos (damage spreading) will happen. We provide a formal proof for this formula, and empirically show that its predictions are accurate. Previous work only works for special cases of balanced families. It has been observed that these characterizations fail for unbalanced families, yet such families are widespread in real biological networks.
If observations confirm BICEP2s claim of a tensor-scalar ratio $rapprox 0.2$ on CMB scales, then the inflationary consistency relation $n_{t}=-r/8$ predicts a small negative value for the tensor spectral index $n_t$. We show that future CMB polarizat
ion experiments should be able to confirm this prediction at several sigma. We also show how to properly extend the consistency relation to solar system scales, where the primordial gravitational wave density $Omega_{gw}$ could be measured by proposed experiments such as the Big Bang Observer. This would provide a far more stringent test of the consistency relation and access much more detailed information about the early universe.
The recent BICEP2 measurement of primordial gravity waves (r = 0.2^{+0.07}_{-0.05}) appears to be in tension with the upper limit from WMAP (r<0.13 at 95% CL) and Planck (r<0.11 at 95% CL). We carefully quantify the level of tension and show that it
is very significant (around 0.1% unlikely) when the observed deficit of large-scale temperature power is taken into account. We show that measurements of TE and EE power spectra in the near future will discriminate between the hypotheses that this tension is either a statistical fluke, or a sign of new physics. We also discuss extensions of the standard cosmological model that relieve the tension, and some novel ways to constrain them.
Predictions of astrochemical models depend strongly on the reaction rate coefficients used in the simulations. We reviewed a number of key reactions for the chemistry of nitrogen-bearing species in the dense interstellar medium and proposed new react
ion rate coefficients for those reactions. The details of the reviews are given in the form of a datasheet associated with each reaction. The new recommended rate coefficients are given with an uncertainty and a temperature range of validity and will be included in KIDA (http://kida.obs.u-bordeaux1.fr).
