Prediction of heat transfer from laminar boundary layers, with emphasis on large free- stream velocity gradients and highly cooled walls

Prediction of heat transfer and shear stress from laminar boundary laye

Macrofaunal community inside and outside of the Darwin Mounds Special Area of Conservation, NE Atlantic

Peer reviewedPublisher PD

Target dependence of the annual modulation in direct dark matter searches

Due to Earth's revolution around the Sun, the expected scattering rate in direct dark matter searches is annually modulated. This modulation is expected to differ between experiments when given as a function of recoil energy $E_\text{R}$, e.g. due to the gravitational focusing effect of the Sun. A better variable to compare results among experiments employing different targets is the minimum speed $v_\text{min}$ a dark matter particle must have to impart a recoil energy $E_\text{R}$ to a target nucleus. It is widely believed that the modulation expressed as a function of $v_\text{min}$ is common to all experiments, irrespective of the dark matter distribution. We point out that the annual modulation as a function of $v_\text{min}$, and in particular the times at which the rate is maximum and minimum, could be very different depending on the detector material. This would be an indication of a scattering cross section with non-factorizable velocity and target material dependence. Observing an annual modulation with at least two different target elements would be necessary to identify this type of cross section.Comment: 6 pages, 4 figures. Version accepted for publicatio

Unified Halo-Independent Formalism From Convex Hulls for Direct Dark Matter Searches

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution $F(v)$ in Earth's frame or 2- Galactic velocity distribution $f^{\rm gal}(\vec{u})$, consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is $({\mathcal N}-1)$, where ${\mathcal N}$ is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is ${\mathcal N}$. Using time-averaged rates, the aforementioned form of $F(v)$ results in a piecewise constant unmodulated halo function $\tilde\eta^0_{BF}(v_{\rm min})$ (which is an integral of the speed distribution) with at most $({\mathcal N}-1)$ downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of $f^{\rm gal}(\vec{u})$, which is a sum of Galactic streams, yields a periodic time-dependent halo function $\tilde\eta_{BF}(v_{\rm min}, t)$ which at any fixed time is a piecewise constant function of $v_{\rm min}$ with at most ${\mathcal N}$ downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic ...Comment: v2: Published version. Text altered, conclusions unchanged. v1: 30 pages, 7 figure

Assessing Compatibility of Direct Detection Data: Halo-Independent Global Likelihood Analyses

We present two different halo-independent methods to assess the compatibility of several direct dark matter detection data sets for a given dark matter model using a global likelihood consisting of at least one extended likelihood and an arbitrary number of Gaussian or Poisson likelihoods. In the first method we find the global best fit halo function (we prove that it is a unique piecewise constant function with a number of down steps smaller than or equal to a maximum number that we compute) and construct a two-sided pointwise confidence band at any desired confidence level, which can then be compared with those derived from the extended likelihood alone to assess the joint compatibility of the data. In the second method we define a "constrained parameter goodness-of-fit" test statistic, whose $p$-value we then use to define a "plausibility region" (e.g. where $p \geq 10\%$). For any halo function not entirely contained within the plausibility region, the level of compatibility of the data is very low (e.g. $p < 10 \%$). We illustrate these methods by applying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particles with elastic spin-independent isospin-conserving interactions or exothermic spin-independent isospin-violating interactions.Comment: 31 pages, 6 figures. V2: Modified several paragraphs to improve clarify. Modified Fig. 5 and added Fig. 6 to further illustrate methods of Section 5. Added proof of uniqueness of best fit halo function in Appendix