Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau(p1) and tau(p2), of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1 tau(eta) to 54T(L), where tau(eta) and T-L are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau(p1), the PDF shape is the fattest for equal-size particles (tau(p2) = tau(p1)), and becomes thinner at both tau(p2) tau(p1). Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) less than or similar to f less than or similar to 1, the PDF fatness first increases with the friction time tau(p,h) of the larger particle, peaks at tau(p,h) similar or equal to tau(eta), and then decreases as tp, h increases further. For 0 > T-L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.Astronom

The Hatsopoulos-Gyftopoulos resolution of the Schroedinger-Park paradox about the concept of "state" in quantum statistical mechanics

A seldom recognized fundamental difficulty undermines the concept of individual ``state'' in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol. 36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol. 6, 15, 127, 439, 561 (1976).Comment: RevTeX4, 7 pages, corrected a paragraph and added an example at page 3, to appear in Mod. Phys. Lett.

Kosmotropes and chaotropes: modelling preferential exclusion, binding and aggregate stability

Kosmotropic cosolvents added to an aqueous solution promote the aggregation of hydrophobic solute particles, while chaotropic cosolvents act to destabilise such aggregates. We discuss the mechanism for these phenomena within an adapted version of the two-state Muller-Lee-Graziano model for water, which provides a complete description of the ternary water/cosolvent/solute system for small solute particles. This model contains the dominant effect of a kosmotropic substance, which is to enhance the formation of water structure. The consequent preferential exclusion both of cosolvent molecules from the solvation shell of hydrophobic particles and of these particles from the solution leads to a stabilisation of aggregates. By contrast, chaotropic substances disrupt the formation of water structure, are themselves preferentially excluded from the solution, and thereby contribute to solvation of hydrophobic particles. We use Monte Carlo simulations to demonstrate at the molecular level the preferential exclusion or binding of cosolvent molecules in the solvation shell of hydrophobic particles, and the consequent enhancement or suppression of aggregate formation. We illustrate the influence of structure-changing cosolvents on effective hydrophobic interactions by modelling qualitatively the kosmotropic effect of sodium chloride and the chaotropic effect of urea.Comment: 13 pages, 12 figures; inclusion of review material, parameter analysis and comparison of kosmotropic and chaotropic effect

Astrophysical signatures of boson stars: quasinormal modes and inspiral resonances

Compact bosonic field configurations, or boson stars, are promising dark matter candidates which have been invoked as an alternative description for the supermassive compact objects in active galactic nuclei. Boson stars can be comparable in size and mass to supermassive black holes and they are hard to distinguish by electromagnetic observations. However, boson stars do not possess an event horizon and their global spacetime structure is different from that of a black hole. This leaves a characteristic imprint in the gravitational-wave emission, which can be used as a discriminant between black holes and other horizonless compact objects. Here we perform a detailed study of boson stars and their gravitational-wave signatures in a fully relativistic setting, a study which was lacking in the existing literature in many respects. We construct several fully relativistic boson star configurations, and we analyze their geodesic structure and free oscillation spectra, or quasinormal modes. We explore the gravitational and scalar response of boson star spacetimes to an inspiralling stellar-mass object and compare it to its black hole counterpart. We find that a generic signature of compact boson stars is the resonant-mode excitation by a small compact object on stable quasi-circular geodesic motion.Comment: 20 pages, 8 figures. v2: minor corrections, version to be published in Phys. Rev. D. v3: final versio

Dark matter and the first stars: a new phase of stellar evolution

A mechanism is identified whereby dark matter (DM) in protostellar halos dramatically alters the current theoretical framework for the formation of the first stars. Heat from neutralino DM annihilation is shown to overwhelm any cooling mechanism, consequently impeding the star formation process and possibly leading to a new stellar phase. A "dark star'' may result: a giant ($\gtrsim 1$ AU) hydrogen-helium star powered by DM annihilation instead of nuclear fusion. Observational consequences are discussed.Comment: 5 pages, 2 figures; replaced with accepted versio

Estimates of the steady state growth rates for the Scandinavian countries: a knowledge economy approach

This paper estimates the steady state growth rate for Scandinavian countries with a “knowledge economy” approach. We shall use an extended version of the Solow (1956) growth model, in which total factor productivity is assumed to be a function of human capital (measured by average years of education), trade openness and investment ratio. Using this framework we show that these factors, and in particular the education variable, have played an important role to determine the long run growth rates of the Scandinavian countries. Some policy measures are identified to improve the long-run growth rates for these countries.Endogenous growth models, Trade openness, human capital, investment ratio, Steady state growth rate, Scandinavian countr

Neutralino with the Right Cold Dark Matter Abundance in (Almost) Any Supersymmetric Model

We consider non-standard cosmological models in which the late decay of a scalar field $\phi$ reheats the Universe to a low reheating temperature, between 5 MeV and the standard freeze-out temperature of neutralinos of mass $m_{\chi}$. We point out that in these models all neutralinos with standard density $\Omega_{\rm std} \gtrsim 10^{-5} (100 {\rm GeV}/m_\chi)$ can have the density of cold dark matter, provided the right combination of the following two parameters can be achieved in the high energy theory: the reheating temperature, and the ratio of the number of neutralinos produced per $\phi$ decay over the $\phi$ field mass. We present the ranges of these parameters where a combination of thermal and non-thermal neutralino production leads to the desired density, as functions of $\Omega_{\rm std}$ and $m_{\chi}$.Comment: 4 pages, 1 figur

Update on Light WIMP Limits: LUX, lite and Light

We reexamine the current direct dark matter data including the recent CDMSlite and LUX data, assuming that the dark matter consists of light WIMPs, with mass close to 10 GeV/$c^2$ with spin-independent and isospin-conserving or isospin-violating interactions. We compare the data with a standard model for the dark halo of our galaxy and also in a halo-independent manner. In our standard-halo analysis, we find that for isospin-conserving couplings, CDMSlite and LUX together exclude the DAMA, CoGeNT, CDMS-II-Si, and CRESST-II possible WIMP signal regions. For isospin-violating couplings instead, we find that a substantial portion of the CDMS-II-Si region is compatible with all exclusion limits. In our halo-independent analysis, we find that for isospin-conserving couplings, the situation is of strong tension between the positive and negative results, as it was before the LUX and CDMSlite bounds, which turn out to exclude the same possible WIMP signals as previous limits. For isospin-violating couplings, we find that LUX and CDMS-II-Si bounds together exclude or severely constrain the DAMA, CoGeNT and CRESST-II possible WIMP signals.Comment: 15 pages, 15 figures. v2: minor revisions and CoGeNT 2014 data adde