Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach

A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. A high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At the investigated impact conditions compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment

Collapse of the Gd3+Gd^{3+} ESR fine structure throughout the coherent temperature of the Gd-doped Kondo Semiconductor CeFe4P12CeFe_{4}P_{12}

Experiments on the $Gd^{3+}$ Electron Spin Resonance (ESR) in the filled skutterudite $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ ($x \approx 0.001$), at temperatures where the host resistivity manifests a smooth insulator-metal crossover, provides evidence of the underlying Kondo physics associated with this system. At low temperatures (below $T \approx K$), $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ behaves as a Kondo-insulator with a relatively large hybridization gap, and the $Gd^{3+}$ ESR spectra displays a fine structure with lorentzian line shape, typical of insulating media. The electronic gap is attributed to the large hybridization present in the coherent regime of a Kondo lattice, when Ce 4f-electrons cooperate with band properties at half-filling. Mean-field calculations suggest that the electron-phonon interaction is fundamental at explaining the strong 4f-electron hybridization in this filled skutterudite. The resulting electronic structure is strongly temperature dependent, and at about $T^{*} \approx 160 K$ the system undergoes an insulator-to-metal transition induced by the withdrawal of 4f-electrons from the Fermi volume, the system becoming metallic and non-magnetic. The $Gd^{3+}$ ESR fine structure coalesces into a single dysonian resonance, as in metals. Still, our simulations suggest that exchange-narrowing via the usual Korringa mechanism, alone, is not capable of describing the thermal behavior of the ESR spectra in the entire temperature region ($4.2$ - $300$ K). We propose that temperature activated fluctuating-valence of the Ce ions is the missing ingredient that, added to the usual exchange-narrowing mechanism, fully describes this unique temperature dependence of the $Gd^{3+}$ ESR fine structure observed in $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$.Comment: 19 pages, 6 figure

Harper operators, Fermi curves, and Picard-Fuchs equations

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.Comment: v2, 13 pages, minor changes have been mad

Turbulent dissipation in the ISM: the coexistence of forced and decaying regimes and implications for galaxy formation and evolution

We discuss the dissipation of turbulent kinetic energy Ek in the global ISM by means of 2-D, MHD, non-isothermal simulations in the presence of model radiative heating and cooling. We argue that dissipation in 2D is representative of that in three dimensions as long as it is dominated by shocks rather than by a turbulent cascade. Energy is injected at a few isolated sites in space, over relatively small scales, and over short time periods. This leads to the coexistence of forced and decaying regimes in the same flow. We find that the ISM-like flow dissipates its turbulent energy rapidly. In simulations with forcing, the input parameters are the radius l_f of the forcing region, the total kinetic energy e_k each source deposits into the flow, and the rate of formation of those regions, sfr_OB. The global dissipation time t_d depends mainly on l_f. In terms of measurable properties of the ISM, t_d >= Sigma_g u_rms^2/(e_k sfr_OB), where Sigma_g is the average gas surface density and u_rms is the rms velocity dispersion. For the solar neighborhood, t_d >= 1.5x10^7 yr. The global dissipation time is consistently smaller than the crossing time of the largest energy-containing scales. In decaying simulations, Ek decreases with time as t^-n, where n~0.8-0.9. This suggests a decay with distance d as Ek\propto d^{-2n/(2-n)} in the mixed forced+decaying case. If applicable to the vertical direction, our results support models of galaxy evolution in which stellar energy injection provides significant support for the gas disk thickness, but not models of galaxy formation in which this energy injection is supposed to reheat an intra-halo medium at distances of up to 10-20 times the optical galaxy size, as the dissipation occurs on distances comparable to the disk height.Comment: 23 pages, including figures. To appear in ApJ. Abstract abridge

How different Fermi surface maps emerge in photoemission from Bi2212

We report angle-resolved photoemission spectra (ARPES) from the Fermi energy ($E_F$) over a large area of the ($k_x,k_y$) plane using 21.2 eV and 32 eV photons in two distinct polarizations from an optimally doped single crystal of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212), together with extensive first-principles simulations of the ARPES intensities. The results display a wide-ranging level of accord between theory and experiment and clarify how myriad Fermi surface (FS) maps emerge in ARPES under various experimental conditions. The energy and polarization dependences of the ARPES matrix element help disentangle primary contributions to the spectrum due to the pristine lattice from those arising from modulations of the underlying tetragonal symmetry and provide a route for separating closely placed FS sheets in low dimensional materials.Comment: submitted to PR

A New Shear Estimator for Weak Lensing Observations

We present a new shear estimator for weak lensing observations which properly accounts for the effects of a realistic point spread function (PSF). Images of faint galaxies are subject to gravitational shearing followed by smearing with the instrumental and/or atmospheric PSF. We construct a `finite resolution shear operator' which when applied to an observed image has the same effect as a gravitational shear applied prior to smearing. This operator allows one to calibrate essentially any shear estimator. We then specialize to the case of weighted second moment shear estimators. We compute the shear polarizability which gives the response of an individual galaxy's polarization to a gravitational shear. We then compute the response of the population of galaxies, and thereby construct an optimal weighting scheme for combining shear estimates from galaxies of various shapes, luminosities and sizes. We define a figure of merit --- an inverse shear variance per unit solid angle --- which characterizes the quality of image data for shear measurement. The new method is tested with simulated image data. We discuss the correction for anisotropy of the PSF and propose a new technique involving measuring shapes from images which have been convolved with a re-circularizing PSF. We draw attention to a hitherto ignored noise related bias and show how this can be analyzed and corrected for. The analysis here draws heavily on the properties of real PSF's and we include as an appendix a brief review, highlighting those aspects which are relevant for weak lensing.Comment: 39 pages, 9 figure