In Favor of Rigor and Relevance. A Reply to Mark Blaug

The paper discusses Mark Blaug’s recent criticisms of “Sraffian economics”. It is shown that none of the criticisms stand up to close examination. Blaug commits a number of elementary blunders and mistakes the mathematical form of an argument for its content. He variously contradicts himself and puts forward bold contentions that cannot be sustained. The paper concludes with an obvious plea for rigor and relevance.Piero Sraffa;Mark Blaug; General Equilibrium

The faintest galaxies

We investigate the nature of Ultra Faint dwarf spheroidal galaxies (UF dSphs) in a general cosmological context, simultaneously accounting for various "classical" dSphs and Milky Way (MW) properties, including their Metallicity Distribution Function (MDF). The model successfully reproduces both the observed [Fe/H]-Luminosity relation and the mean MDF of UFs. According to our results UFs are the living fossils of H2-cooling minihaloes formed at z>8.5, i.e. before the end of reionization. They are the oldest and the most dark matter-dominated (M/L > 100) dSphs in the MW system, with a total mass of M = 10^(7-8) Msun. The model allows to interpret the different shape of UFs and classical dSphs MDF, along with the frequency of extremely metal-poor stars in these objects. We discuss the "missing satellites problem" by comparing the UF star formation efficiencies with those derived for minihaloes in the Via Lactea simulation.Comment: To appear in the conference proceeding: "First Stars and Galaxies: Challenges in the Next Decade" . Publisher: American Institute of Physics. Editors: V. Bromm, D. Whalen, N. Yoshid

Initial mass function of intermediate mass black hole seeds

We study the Initial Mass Function (IMF) and host halo properties of Intermediate Mass Black Holes (IMBH, 10^{4-6} Msun) formed inside metal-free, UV illuminated atomic cooling haloes (virial temperature T_vir > 10^4 K) either via the direct collapse of the gas or via an intermediate Super Massive Star (SMS) stage. We achieve this goal in three steps: (a) we derive the gas accretion rate for a proto-SMS to undergo General Relativity instability and produce a direct collapse black hole (DCBH) or to enter the ZAMS and later collapse into a IMBH; (b) we use merger-tree simulations to select atomic cooling halos in which either a DCBH or SMS can form and grow, accounting for metal enrichment and major mergers that halt the growth of the proto-SMS by gas fragmentation. We derive the properties of the host halos and the mass distribution of black holes at this stage, and dub it the "Birth Mass Function"; (c) we follow the further growth of the DCBH due to accretion of leftover gas in the parent halo and compute the final IMBH mass.We consider two extreme cases in which minihalos (T_vir < 10^4 K) can (fertile) or cannot (sterile) form stars and pollute their gas leading to a different IMBH IMF. In the (fiducial) fertile case the IMF is bimodal extending over a broad range of masses, M= (0.5-20)x10^5 Msun, and the DCBH accretion phase lasts from 10 to 100 Myr. If minihalos are sterile, the IMF spans the narrower mass range M= (1-2.8)x10^6 Msun, and the DCBH accretion phase is more extended (70-120 Myr). We conclude that a good seeding prescription is to populate halos (a) of mass 7.5 < log (M_h/Msun) < 8, (b) in the redshift range 8 < z < 17, (c) with IMBH in the mass range 4.75 < log (M_BH/Msun) < 6.25.Comment: MNRAS, in press. Comments welcom

Galaxy formation with radiative and chemical feedback

Here we introduce GAMESH, a novel pipeline which implements self-consistent radiative and chemical feedback in a computational model of galaxy formation. By combining the cosmological chemical-evolution model GAMETE with the radiative transfer code CRASH, GAMESH can post process realistic outputs of a N-body simulation describing the redshift evolution of the forming galaxy. After introducing the GAMESH implementation and its features, we apply the code to a low-resolution N-body simulation of the Milky Way formation and we investigate the combined effects of self-consistent radiative and chemical feedback. Many physical properties, which can be directly compared with observations in the Galaxy and its surrounding satellites, are predicted by the code along the merger-tree assembly. The resulting redshift evolution of the Local Group star formation rates, reionisation and metal enrichment along with the predicted Metallicity Distribution Function of halo stars are critically compared with observations. We discuss the merits and limitations of the first release of GAMESH, also opening new directions to a full implementation of feedback processes in galaxy formation models by combining semi-analytic and numerical methods.Comment: This version has coloured figures not present in the printed version. Submitted to MNRAS, minor revision

White Elephants and Other Non-basic Commodities: Piero Sraffa and Krishna Bharadwaj on the Role and Significance of the Distinction between Basics and Non-basics:

After the publication of Production of Commodities by Means of Commodities ( Sraffa, 1960 ), a lot of attention was devoted to 'reswitching', that is to the fact that a technique is cost-minimising at two disconnected ranges of the rate of profits and not so in between these ranges. We owe Krishna Bharadwaj (1970, Schweizerische Zeitschrift für Volkswirtschaft und Statistik, 106, 409–429) an important contribution to the debate by stating and proving a general result concerning the maximum number of switches between two techniques that have at least one switch point on the wage-frontier. She proved that the maximum number of switches coincides with the number of distinct commodities, without double counting, that enter directly or indirectly into at least one of the alternative methods of production. This means that if the alternative methods produce a commodity that is basic in both techniques, then non-basics in both techniques play no role in this, whereas if the alternative methods produce a non-basic commodity in at least one technique, then a role is played also by those non-basics that enter directly or indirectly into the production of at least one of the alternative methods of production. JEL Code: B12, B21, B31, B51, D24, D5

The Brightest Lyα\alpha Emitter: Pop III or Black Hole?

CR7 is the brightest $z=6.6 \, {\rm Ly}\alpha$ emitter (LAE) known to date, and spectroscopic follow-up by Sobral et al. (2015) suggests that CR7 might host Population (Pop) III stars. We examine this interpretation using cosmological hydrodynamical simulations. Several simulated galaxies show the same "Pop III wave" pattern observed in CR7. However, to reproduce the extreme CR7 ${\rm Ly}\alpha$/HeII1640 line luminosities ($L_{\rm \alpha/He II}$) a top-heavy IMF and a massive ($>10^{7}{\rm M}_{\odot}$) PopIII burst with age $<2$ Myr are required. Assuming that the observed properties of ${\rm Ly}\alpha$ and HeII emission are typical for Pop III, we predict that in the COSMOS/UDS/SA22 fields, 14 out of the 30 LAEs at $z=6.6$ with $L_{\alpha} >10^{43.3}{\rm erg}\,{\rm s}^{-1}$ should also host Pop III stars producing an observable $L_{\rm He II}>10^{42.7}{\rm erg}\,{\rm s}^{-1}$. As an alternate explanation, we explore the possibility that CR7 is instead powered by accretion onto a Direct Collapse Black Hole (DCBH). Our model predicts $L_{\alpha}$, $L_{\rm He II}$, and X-ray luminosities that are in agreement with the observations. In any case, the observed properties of CR7 indicate that this galaxy is most likely powered by sources formed from pristine gas. We propose that further X-ray observations can distinguish between the two above scenarios.Comment: 6 pages, 4 figure

Computational modeling of Li-ion batteries

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Cross-Border Investment, Conflict of Laws, and the Privatization of Securities Law

The rapid acceleration of transnational investing is occurring in an environment in which emerging markets, and foreign interest in these markets, are exploding. The issues involved with cross-border investment, conflict of laws and the privatization of securities law are examined

Thermo-Hydrodynamic Analysis of Plain and Tilting Pad Bearings

Abstract The demand for higher efficiency and increased equipment compactness is pushing industrial compressors' designers towards the choice of higher rotor peripheral speed. As a consequence, modern bearing-rotor systems are subject to complex thermal phenomena inducing a renewed interest on their real working conditions. This work is about the validation of the in-house numerical code TILTPAD developed at the Department of Industrial Engineering of the University of Florence for the thermo-hydrodynamic analysis of both plain and tilting pad journal bearings performance. TILTPAD is a steady-state code based on a 2D thin-film approach able to find either the resulting hydrodynamic load using the shaft equilibrium position and the rotational speed (i.e., direct problem) or the shaft equilibrium position once the load and the rotational speed are prescribed (i.e., inverse problem). In order to calculate pads' pressure distribution a finite element approach is used to solve the Reynolds equation together with a mixed procedure to evaluate pads equilibrium positions. Two steady-state energy equations based on a Petroff-type simplification are implemented in the code. The first one is proposed in the work of Balbahadur and Kirk [1] while the second one is based on an improved mixing model and a temperature dependent viscosity. An iterative procedure is used between Reynolds and energy equations to account for the dependence of the dynamic viscosity on the temperature field. Super-laminar flow regimes are also modeled in the code by means of a simplified approach able to represents, with reasonable accuracy, the effects of Taylor-Couette vortex flows and of the transitional regimes up to the onset of a fully turbulent state. Under these hypotheses, the pressure field is slightly affected by the viscosity variation while dissipative effects are enhanced. The code has been validated by means of comparison with available experimental data. Particular attention is devoted to static working parameters (i.e., equilibrium position and frictional power loss), reproducing the global behavior of the bearing, although some local characteristic is also considered

Deep into the structure of the first galaxies: SERRA views

We study the formation and evolution of a sample of Lyman Break Galaxies in the Epoch of Reionization by using high-resolution ($\sim 10 \,{\rm pc}$), cosmological zoom-in simulations part of the SERRA suite. In SERRA, we follow the interstellar medium (ISM) thermo-chemical non-equilibrium evolution, and perform on-the-fly radiative transfer of the interstellar radiation field (ISRF). The simulation outputs are post-processed to compute the emission of far infrared lines ([CII], [NII], and [OIII]). At $z=8$, the most massive galaxy, `Freesia', has an age $t_\star \simeq 409\,{\rm Myr}$, stellar mass $M_{\star} \simeq 4.2\times 10^9 {\rm M}_{\odot}$, and a star formation rate ${\rm SFR} \simeq 11.5\,{\rm M}_{\odot}{\rm yr}^{-1}$, due to a recent burst. Freesia has two stellar components (A and B) separated by $\simeq 2.5\, {\rm kpc}$; other 11 galaxies are found within $56.9 \pm 21.6 \, {\rm kpc}$. The mean ISRF in the Habing band is $G = 7.9\, G_0$ and is spatially uniform; in contrast, the ionisation parameter is $U = 2^{+20}_{-2} \times 10^{-3}$, and has a patchy distribution peaked at the location of star-forming sites. The resulting ionising escape fraction from Freesia is $f_{\rm esc}\simeq 2\%$. While [CII] emission is extended (radius 1.54 kpc), [OIII] is concentrated in Freesia-A (0.85 kpc), where the ratio $\Sigma_{\rm [OIII]}/\Sigma_{\rm [CII]} \simeq 10$. As many high-$z$ galaxies, Freesia lies below the local [CII]-SFR relation. We show that this is the general consequence of a starburst phase (pushing the galaxy above the Kennicutt-Schmidt relation) which disrupts/photodissociates the emitting molecular clouds around star-forming sites. Metallicity has a sub-dominant impact on the amplitude of [CII]-SFR deviations.Comment: 22 pages, 14 figures, accepted by MNRA