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Using an empirical pseudopotential description of electron states and an adiabatic bond charge model for phonon states in bulk silicon, we theoretically investigate two-photon indirect optical injection of carriers and spins and two-color coherent control of the motion of the injected carriers and spins. For two-photon indirect carrier and spin injection, we identify the selection rules of band edge transitions, the injection in each conduction band valley, and the injection from each phonon branch at 4 K and 300 K. At 4 K, the TA phonon-assisted transitions dominate the injection at low photon energies, and the TO phonon-assisted at high photon energies. At 300 K, the former dominates at all photon energies of interest. The carrier injection shows anisotropy and linear-circular dichroism with respect to light propagation direction. For light propagating along the $<001>$ direction, the carrier injection exhibits valley anisotropy, and the injection into the $Z$ conduction band valley is larger than that into the $X/Y$ valleys. For $��^-$ light propagating along the $<001>$ ($<111>$) direction, the degree of spin polarization gives a maximum value about 20% (6%) at 4 K and -10% (20%) at 300 K, and at both temperature shows abundant structure near the injection edges due to contributions from different phonon branches. Forthe two-color coherent current injection with an incident optical field composed of a fundamental frequency and its second harmonic, the response tensors of the electron (hole) charge and spin currents are calculated at 4 K and 300 K. We show the current control for three different polarization scenarios. The spectral dependence of the maximum swarm velocity shows that the direction of charge current reverses under increase in photon energy. 15 pages and 14 figures

We present preliminary results on a study of the 2--850 micron SEDs of a sample of 30 FIRBACK galaxies selected at 170 micron. These sources are representative of the brightest ~10% of the Cosmic Infrared Background. They are a mixture of mostly local (z<~0.3) starforming galaxies, and a tail of ULIGs that extend up to z~1, and are likely to be a similar population to faint SCUBA sources. We use archival Spitzer IRAC and MIPS data to extend the spectral coverage to the mid-IR regime, resulting in an unprecended (for this redshift range) census of their infrared SEDs. This allows us to study in far greater detail this important population linking the near-IR stellar emission with PAH and thermal dust emission. We do this using a Markov Chain Monte Carlo method, which easily allows for the inclusion of ~6 free parameters, as well as an estimate of parameter uncertainties and correlations. Comment: 5 pages, 3 figures. Proceeding for the conference "Starbursts: From 30 Doradus to Lyman Break Galaxies", held in Cambridge (UK) in September, 2004

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic fragility transition and the locus of specific heat maxima $C_P^{\rm max}$ (``Widom line'') emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between $C_P^{\rm max}$ and dynamic crossover is not limited to the case of water, a hydrogen bond network forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically-symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions. Comment: 6 pages and 5 figures

A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we prove {\it a priori} bounds. They imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values. Comment: LaTeX, 29 pages, 2 figures

A domain $R$ is said to have the finite factorization property if every nonzero non-unit element of $R$ has at least one and at most finitely many distinct factorizations up to multiplication of irreducible factors by central units. Let $k$ be an algebraically closed field and let $A$ be a $k$-algebra. We show that if $A$ has an associated graded ring that is a domain with the property that the dimension of each homogeneous component is finite then $A$ is a finite factorization domain. As a corollary, we show that many classes of algebras have the finite factorization property, including Weyl algebras, enveloping algebras of finite-dimensional Lie algebras, quantum affine spaces and shift algebras. This provides a termination criterion for factorization procedures over these algebras. In addition, we give explicit upper bounds on the number of distinct factorizations of an element in terms of data from the filtration.

We first prove decay estimates and spacetime integral bounds for Stokes flows in amalgam spaces $E^r_q$ which connect the classical Lebesgue spaces to the spaces of uniformly locally $r$-integrable functions. Using these estimates, we construct mild solutions of the Navier-Stokes equations in the amalgam spaces satisfying the corresponding spacetime integral bounds. Time-global solutions are constructed for small data in $E^3_q$, $1\le q \le 3$. Our results provide new bounds for the strong solutions classically constructed by Kato and the more recent solutions in uniformly local spaces constructed by Maekawa and Terasawa. As an application we obtain a result on the stability of suitability for weak solutions to the perturbed Navier-Stokes equation where the drift velocity solves the Navier-Stokes equations and has small data in a local $L^3$ class. Extending an earlier result, we also construct global-in-time local energy weak solutions in $E^2_q$, $1\le q <2$. 57 pages, 1 figure

We provide a non-explicit separation of the number-on-forehead communication complexity classes RP and NP when the number of players is up to \delta log(n) for any \delta<1. Recent lower bounds on Set-Disjointness [LS08,CA08] provide an explicit separation between these classes when the number of players is only up to o(loglog(n)).

Differential settling and growth of dust grains impact the structure of the radiative envelopes of gaseous planets during formation. Sufficiently rapid dust growth can result in envelopes with substantially reduced opacities for radiation transport, thereby facilitating planet formation. We revisit the problem and establish that dust settling and grain growth also lead to outer planetary envelopes that are prone to compositional instabilities, by virtue of their inverted mean-molecular weight gradients. Under a variety of conditions, we find that the radiative envelopes of forming planets experience compositional turbulence driven by a semi-transparent version of the thermohaline instability ('fingering convection'). The compositional turbulence seems efficient at mixing dust in the radiative envelopes of planets forming at super-AU distances (say $5$ AU) from a Sun-like star, but not so at sub-AU distances (say $0.2$ AU). We also address the possibility of compositional layering in this context. Distinct turbulent regimes for planetary envelopes growing at sub-AU vs. super-AU distances could leave an imprint on the final planets formed. Comment: 9 pages, MNRAS accepted

Scattering amplitudes of partons in QCD contain infrared divergences which can be resummed to all orders in terms of an anomalous dimension. Independently, in the limit of high-energy forward scattering, large logarithms of the energy can be resummed using Balitsky-Fadin-Kuraev-Lipatov theory. We use the latter to analyze the infrared-singular part of amplitudes to all orders in perturbation theory and to next-to-leading-logarithm accuracy in the high-energy limit, resumming the two-Reggeon contribution. Remarkably, we find a closed form for the infrared-singular part, predicting the Regge limit of the soft anomalous dimension to any loop order. Comment: 35 pages, 8 figures

Big Data has become prominent throughout many scientific fields, and as a result, scientific communities have sought out Big Data frameworks to accelerate the processing of their increasingly data-intensive pipelines. However, while scientific communities typically rely on High-Performance Computing (HPC) clusters for the parallelization of their pipelines, many popular Big Data frameworks such as Hadoop and Apache Spark were primarily designed to be executed on dedicated commodity infrastructures. This paper evaluates the benefits of pilot jobs over traditional batch submission for Apache Spark on HPC clusters. Surprisingly, our results show that the speed-up provided by pilot jobs over batch scheduling is moderate to non-existent (0.98 on average) despite the presence of long queuing times. In addition, pilot jobs provide an extra layer of scheduling that complicates debugging and deployment. We conclude that traditional batch scheduling should remain the default strategy to deploy Apache Spark applications on HPC clusters.