Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas

We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations

The Darkest Shadows: Deep Mid-Infrared Extinction Mapping of a Massive Protocluster

We use deep $8\:\mu m$ Spitzer-IRAC imaging of a massive Infrared Dark Cloud (IRDC) G028.37+00.07 to construct a Mid-Infrared (MIR) extinction map that probes mass surface densities up to $\Sigma\:\sim 1\:\rm{g~cm^{-2}}$ ($A_V\sim200\:$mag), amongst the highest values yet probed by extinction mapping. Merging with a NIR extinction map of the region, creates a high dynamic range map that reveals structures down to $A_V\sim1\:$mag. We utilize the map to: (1) Measure a cloud mass $\sim7\times10^4\:M_\odot$ within a radius of $\sim8\:$pc. $^{13}$CO kinematics indicate that the cloud is gravitationally bound. It thus has the potential to form one of the most massive young star clusters known in the Galaxy. (2) Characterize the structures of 16 massive cores within the IRDC, finding they can be fit by singular polytropic spheres with $\rho\propto{r}^{-k_\rho}$ and $k_\rho=1.3\pm0.3$. They have $\overline{\Sigma}\simeq0.1-0.4\:\rm{g~cm^{-2}}$ --- relatively low values that, along with their measured cold temperatures, suggest magnetic fields, rather than accretion-powered radiative heating, are important for controlling fragmentation of these cores. (3) Determine the $\Sigma$ (equivalently column density or $A_V$) probability distribution function (PDF) for a region that is near complete for $A_V>3\:$mag. The PDF is well fit by a single log-normal with mean $\overline{A}_V\simeq9\:$mag, high compared to other known clouds. It does not exhibit a separate high-end power law tail, which has been claimed to indicate the importance of self-gravity. However, we suggest that the PDF does result from a self-similar, self-gravitating hierarchy of structure being present over a wide range of scales in the cloud.Comment: 6 pages, 3 figures, 1 table, accepted to ApJ

Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems

In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel Monte Carlo (MLMC) methods. The former provides a hierarchy of approximations of different resolution, whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels. The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost, and to efficiently generate samples at different levels. In particular, it is cheap to generate samples on coarse grids but with low resolution, and it is expensive to generate samples on fine grids with high accuracy. By suitably choosing the number of samples at different levels, one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces, while retaining the accuracy of the final Monte Carlo estimate. Further, we describe a multilevel Markov chain Monte Carlo method, which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids, while combining the samples at different levels to arrive at an accurate estimate. The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in \cite{ketelson2013}, and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates.Comment: 29 pages, 6 figure

On the location of plumes and lateral movement of thermochemical structures with high bulk modulus in the 3-D compressible mantle

The two large low shear velocity provinces (LLSVPs) at the base of the lower mantle are prominent features in all shear wave tomography models. Various lines of evidence suggest that the LLSVPs are thermochemical and are stable on the order of hundreds of million years. Hot spots and large igneous province eruption sites tend to cluster around the edges of LLSVPs. With 3-D global spherical dynamic models, we investigate the location of plumes and lateral movement of chemical structures, which are composed of dense, high bulk modulus material. With reasonable values of bulk modulus and density anomalies, we find that the anomalous material forms dome-like structures with steep edges, which can survive for billions of years before being entrained. We find that more plumes occur near the edges, rather than on top, of the chemical domes. Moreover, plumes near the edges of domes have higher temperatures than those atop the domes. We find that the location of the downwelling region (subduction) controls the direction and speed of the lateral movement of domes. Domes tend to move away from subduction zones. The domes could remain relatively stationary when distant from subduction but would migrate rapidly when a new subduction zone initiates above. Generally, we find that a segment of a dome edge can be stationary for 200 million years, while other segments have rapid lateral movement. In the presence of time-dependent subduction, the computations suggest that maintaining the lateral fixity of the LLSVPs at the core-mantle boundary for longer than hundreds of million years is a challenge

Mobile telephony and internet growth: impacts on consumer welfare

Innovation in digital technology has allowed rapid growth in mobile telephone and Internet adoption among consumers. The implication underlying the high rates of subscription growth is that consumers generally place a high valuation on telecommunication services. Moreover, since mobile telephone and Internet are predominantly telecommunication services, it is reasonable to presume that the network effect may be largely responsible for this growth. The implication of the network effect, where the consumer’s valuation of service increases with the size of the network is that subscription growth is endogenous. However, to date there have been few attempts to measure the change in consumer welfare as networks increase. Following Hausman (1981), this paper measures the change in consumer surplus based on the compensating variations approach. The result is an annual measure of the change in consumer surplus for the representative consumer for the OECD region. In addition, the approach reveals whether marginal consumer surplus is a decreasing or increasing function of network size. Measurement of the change in consumer welfare thus provides an additional tool for public policy analysis.Consumer welfare; network effect; compensating variation

A benchmark study on mantle convection in a 3-D spherical shell using CitcomS

As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 × 10^3 or 10^5) and viscosity contrast due to temperature dependence (1 to 10^7). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger

Slabs in the lower mantle and their modulation of plume formation

Numerical mantle convection models indicate that subducting slabs can reach the core-mantle boundary (CMB) for a wide range of assumed material properties and plate tectonic histories. An increase in lower mantle viscosity, a phase transition at 660 km depth, depth-dependent thermal expansivity, and depth-dependent thermal diffusivity do not preclude model slabs from reaching the CMB. We find that ancient slabs could be associated with lateral temperature anomalies ~500°C cooler than ambient mantle. Plausible increases of thermal conductivity with depth will not cause slabs to diffuse away. Regional spherical models with actual plate evolutionary models show that slabs are unlikely to be continuous from the upper mantle to the CMB, even for radially simple mantle structures. The observation from tomography showing only a few continuous slab-like features from the surface to the CMB may be a result of complex plate kinematics, not mantle layering. There are important consequences of deeply penetrating slabs. Our models show that plumes preferentially develop on the edge of slabs. In areas on the CMB free of slabs, plume formation and eruption are expected to be frequent while the basal thermal boundary layer would be thin. However, in areas beneath slabs, the basal thermal boundary layer would be thicker and plume formation infrequent. Beneath slabs, a substantial amount of hot mantle can be trapped over long periods of time, leading to “mega-plume” formation. We predict that patches of low seismic velocity may be found beneath large-scale high seismic velocity structures at the core-mantle boundary. We find that the location, buoyancy, and geochemistry of mega-plumes will differ from those plumes forming at the edge of slabs. Various geophysical and geochemical implications of this finding are discussed