Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

Thermoelectric properties of lead chalcogenide core-shell nanostructures

We present the full thermoelectric characterization of nanostructured bulk PbTe and PbTe-PbSe samples fabricated from colloidal core-shell nanoparticles followed by spark plasma sintering. An unusually large thermopower is found in both materials, and the possibility of energy filtering as opposed to grain boundary scattering as an explanation is discussed. A decreased Debye temperature and an increased molar specific heat are in accordance with recent predictions for nanostructured materials. On the basis of these results we propose suitable core-shell material combinations for future thermoelectric materials of large electric conductivities in combination with an increased thermopower by energy filtering.Comment: 12 pages, 8 figure

Optimal leverage from non-ergodicity

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of ergodicit

First In-Situ Measurements of Plume Chemistry at Mount Garet Volcano, Island of Gaua (Vanuatu)

Recent volcanic gas compilations have urged the need to expand in-situ plume measurements to poorly studied, remote volcanic regions. Despite being recognized as one of the main volcanic epicenters on the planet, the Vanuatu arc remains poorly characterized for its subaerial emissions and their chemical imprints. Here, we report on the first plume chemistry data for Mount Garet, on the island of Gaua, one of the few persistent volatile emitters along the Vanuatu arc. Data were collected with a multi-component gas analyzer system (multi-GAS) during a field campaign in December 2018. The average volcanic gas chemistry is characterized by mean molar CO2/SO2, H2O/SO2, H2S/SO2 and H2/SO2 ratios of 0.87, 47.2, 0.13 and 0.01, respectively. Molar proportions in the gas plume are estimated at 95.9 ± 11.6, 1.8 ± 0.5, 2.0 ± 0.01, 0.26 ± 0.02 and 0.06 ± 0.01, for H2O, CO2, SO2, H2S and H2. Using the satellite-based 10-year (2005–2015) averaged SO2 flux of ~434 t d−1 for Mt. Garet, we estimate a total volatile output of about 6482 t d−1 (CO2 ~259 t d−1; H2O ~5758 t d−1; H2S ~30 t d−1; H2 ~0.5 t d−1). This may be representative of a quiescent, yet persistent degassing period at Mt. Garet; whilst, as indicated by SO2 flux reports for the 2009–2010 unrest, emissions can be much higher during eruptive episodes. Our estimated emission rates and gas composition for Mount Garet provide insightful information on volcanic gas signatures in the northernmost part of the Vanuatu Arc Segment. The apparent CO2-poor signature of high-temperature plume degassing at Mount Garet raises questions on the nature of sediments being subducted in this region of the arc and the possible role of the slab as the source of subaerial CO2. In order to better address the dynamics of along-arc volatile recycling, more volcanic gas surveys are needed focusing on northern Vanuatu volcanoes

Gravitational Radiation from Intermediate-Mass Black Holes

Recent X-ray observations of galaxies with ROSAT, ASCA, and Chandra have revealed numerous bright off-center point sources which, if isotropic emitters, are likely to be intermediate-mass black holes, with hundreds to thousands of solar masses. The origin of these objects is under debate, but observations suggest that a significant number of them currently reside in young high-density stellar clusters. There is also growing evidence that some Galactic globular clusters harbor black holes of similar mass, from observations of stellar kinematics. In such high-density stellar environments, the interactions of intermediate-mass black holes are promising sources of gravitational waves for ground-based and space-based detectors. Here we explore the signal strengths of binaries containing intermediate-mass black holes or stellar-mass black holes in dense stellar clusters. We estimate that a few to tens per year of these objects will be detectable during the last phase of their inspiral with the advanced LIGO detector, and up to tens per year will be seen during merger, depending on the spins of the black holes. We also find that if these objects reside in globular clusters then tens of sources will be detectable with LISA from the Galactic globular system in a five year integration, and similar numbers will be detectable from more distant galaxies. The signal strength depends on the eccentricity distribution, but we show that there is promise for strong detection of pericenter precession and Lense-Thirring precession of the orbital plane. We conclude by discussing what could be learned about binaries, dense stellar systems, and strong gravity if such signals are detected.Comment: Minor changes, accepted by ApJ (December 10, 2002

Effect of Condensed Tannin in Lotus Corniculatus and Lotus Pedunculatus on Digestion of Rubisco in the Rumen

The in vitro precipitation of ribulose-1,5-bisphosphate carboxylase (Rubisco) by condensed tannin (CT) extracted from Lotus corniculatus and Lotus pedunculatus and the effect of these CT on the in vitro rumen degradation of Rubisco was used to compare the reactivity of these CT. The chemical structure of CT from Lotus corniculatus was homogenous with epicatechin stereochemistry and mostly procyanidin units. The CT from Lotus pedunculatus was heterogenous with mostly prodelphinidin units. The amount of CT required to precipitate all the Rubisco when total soluble leaf protein was incubated with CT from Lotus corniculatus and Lotus pedunculatus was similar. Although CT from both species were able to reduce the in vitro degradation of Rubisco, CT from Lotus corniculatus was less effective than CT from Lotus pedunculatus at reducing this degradation

Spin-orbit Scattering and the Kondo Effect

The effects of spin-orbit scattering of conduction electrons in the Kondo regime are investigated theoretically. It is shown that due to time-reversal symmetry, spin-orbit scattering does not suppress the Kondo effect, even though it breaks spin-rotational symmetry, in full agreement with experiment. An orbital magnetic field, which breaks time-reversal symmetry, leads to an effective Zeeman splitting, which can be probed in transport measurements. It is shown that, similar to weak-localization, this effect has anomalous magnetic field and temperature dependence.Comment: 10 pages, RevTex, one postscript figure available on request from [email protected]

Electronic Orders Induced by Kondo Effect in Non-Kramers f-Electron Systems

This paper clarifies the microscopic nature of the staggered scalar order, which is specific to even number of f electrons per site. In such systems, crystalline electric field (CEF) can make a singlet ground state. As exchange interaction with conduction electrons increases, the CEF singlet at each site gives way to Kondo singlets. The collective Kondo singlets are identified with itinerant states that form energy bands. Near the boundary of itinerant and localized states, a new type of electronic order appears with staggered Kondo and CEF singlets. We present a phenomenological three-state model that qualitatively reproduces the characteristic phase diagram, which have been obtained numerically with use of the continuous-time quantum Monte Carlo combined with the dynamical mean-field theory. The scalar order observed in PrFe_4P_{12} is ascribed to this staggered order accompanying charge density wave (CDW) of conduction electrons. Accurate photoemission and tunneling spectroscopy should be able to probe sharp peaks below and above the Fermi level in the ordered phase.Comment: 7 pages, 8 figure

Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.Comment: 13 pages, 8 figure