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We study the properties of Lévy flights with index 0 < α < 2 at elapsed times smaller than those required for reaching the diffusive limit, and we focus on the bulk of the walkers' distribution rather than on its tails. On the basis of the analogs of the Kramers–Moyal expansion and of the Pawula theorem, we show that, for any α ≤ 2 / 3 , the bulk of the walkers' distribution occurs at wave-numbers greater than (2 / α) 1 / (2 α) ≥ 1 , and it remains non-self-similar for a time-scale longer than the Markovian time-lag of at least one order of magnitude. This result highlights the fact that for Lévy flights, the Markovianity time-lag is not the only time-scale of the process and indeed another and longer time-scale controls the transition to the familiar power-law regime in the final diffusive limit. The magnitude of this further time-scale is independent of the index α and may compromise the reliability of applications of Lévy flights to real world cases related with recurrence and transience as optimal searching, animal foraging, and site fidelity. [ABSTRACT FROM AUTHOR]

The chemical fingerprints of the first stars are retained within the photospheres of ancient unevolved metal-poor stars. A significant fraction of these stellar fossils is represented by stars known as Carbon-Enhanced Metal-Poor (CEMP), |$\mathrm{[C/Fe]} \gt +0.7$| and |$\mathrm{[Fe/H]} \lt -2$|⁠ , which are likely imprinted by low-energy primordial supernovae. These CEMP stars are largely observed in the Galactic halo and ultrafaint dwarf galaxies, with values reaching |$\rm [C/Fe]=+4.5$|⁠. The Galactic bulge is predicted to host the oldest stars, but it shows a striking dearth of CEMP stars with |$\rm [C/Fe]\gtrsim +2.0$|⁠. Here, we explore the possible reasons for this anomaly by performing a statistical analysis of the observations of metal-poor stars in combination with the predictions of Lambda cold dark matter models. We suggest that the dearth of CEMP stars with high |$\mathrm{[C/Fe]}$| is not due to the low statistics of observed metal-poor stars but is the result of the different formation process of the bulge. N -body simulations show that the first star-forming haloes which end up in the bulge are characterized by the highest star formation rates. These rates enable the formation of rare massive first stars exploding as pair-instability supernovae (PISNe), which wash out the signature of primordial faint supernovae. We demonstrate that the mean |$\mathrm{[C/Fe]}$| of first stars polluted environments decreases with the increasing contribution of PISNe. We conclude that the dearth of CEMP stars in the Galactic bulge indirectly probes the existence of elusive PISNe, and propose a novel method which exploits this lack to constrain the mass distribution of the first stars. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers. [ABSTRACT FROM AUTHOR]

Reply to V P Shkilev. [ABSTRACT FROM AUTHOR]

In this paper, we analyze two effects caused by the Lagrangian nature of turbulent transfer which are usually ignored in the theory of turbulent premixed combustion. These effects are (i) the nonequilibrium behavior of the turbulent diffusion coefficient, which is important for modeling the initial stage of combustion (for example, in the spark ignition engine), and (ii) the existence of a traveling front of turbulent diffusion with finite speed, which controls the velocity of the steady state flame in strong turbulence. However, in order to derive simple and exact results, the hydrodynamical and the combustion subproblems are stated to be independent by assuming a constant density so that a passive chemical reaction is actually considered. First, we derive a parabolic diffusion equation with both diffusion and chemical source terms expressed by Lagrangian characteristics of turbulence. We show that, in general, the diffusivity of product particles is not zero in the moment of their generation by chemical transformation and this result is important for combustion theories that relate the formation of the initial flame with the development of the diffusion coefficient. Afterward, a hyperbolic diffusion equation based on hydrodynamics is derived with turbulent diffusion front velocity Uf=1/2, where 1/2 is the root mean square of turbulent velocity fluctuations, and we analyze the relationships between Uf and the speed of the steady state premixed flame Utss. In particular, for the flamelet combustion mechanism, we obtain Utss=(Uf2+SL2)1/2, where SL is the normal laminar flame speed. This result shows that, in moderate turbulence (1/2∼SL), the usually assumed relation Utss=Uf+SL is not consistent with an accurate statistical analysis and more when Uf≃SL gives a percent error around 40%, which cannot be neglected in applications. In strong turbulence case (1/2>SL), the value of the flame speed is very close to that of the diffusion front velocity. [ABSTRACT FROM AUTHOR]

The article reports on the use of convolution integral of the Mellin transform and the Mellin-Barnes integrals to treat the subordination for the class of self-similar stochastic processes. The author presents the use of notations which turns out to play a basic role in the treatment of the subordination. The Mellin convolution formula plays a noteworthy role in the algebra of random variables, since the probability density of the product of two independent random variables is given by the Mellin convolution of the two corresponding densities.

We investigate the relative dispersion properties of the well-mixed class of Lagrangian stochastic models. Dimensional analysis shows that, given a model in the class, its properties depend solely on a non-dimensional parameter, which measures the relative weight of Lagrangian-to-Eulerian scales. This parameter is formulated in terms of Kolmogorov constants, and model properties are then studied by modifying its value in a range that contains the experimental variability. Large variations are found for the quantity, g* = 2gC, where g is the Richardson constant. [ABSTRACT FROM AUTHOR]

Context. The standard cosmological scenario predicts a hierarchical formation for galaxies. Many substructures have been found in the Galactic halo, usually identified as clumps in kinematic spaces, like the energy-angular momentum space (E − Lz), under the hypothesis that these quantities should be conserved during the interaction. If these clumps also feature different chemical abundances, such as the metallicity distribution function (MDF), these two arguments together (different kinematic and chemical properties) are often used to motivate their association with distinct and independent merger debris. Aims. The aim of this study is to explore to what extent we can couple kinematic characteristics and metallicities of stars in the Galactic halo to reconstruct the accretion history of the Milky Way (MW). In particular, we want to understand whether different clumps in the E − Lz space with different MDFs should be associated with distinct merger debris. Methods. We analysed dissipationless, self-consistent, high-resolution N-body simulations of a MW-type galaxy accreting a satellite with a mass ratio of 1:10, with different orbital parameters and different metallicity gradients, which were assigned a posteriori. Results. We confirm that accreted stars from a ∼1:10 mass ratio merger event redistribute in a wide range of E and Lz, due to the dynamical friction process, and are thus not associated with a single region. Because satellite stars with different metallicities can be deposited in different regions of the E − Lz space (on average the more metal-rich ones end up more gravitationally bound to the MW), this implies that a single accretion of ∼1:10 can manifest with different MDFs, in different regions of the E − Lz space. Conclusions. Groups of stars with different E, Lz, and metallicities may be interpreted as originating from different satellite galaxies, but our analysis shows that these interpretations are not physically motivated. In fact, as we show, the coupling of kinematic information with MDFs to reconstruct the accretion history of the MW can bias the reconstructed merger tree towards increasing the number of past accretions and decreasing the masses of the progenitor galaxies. [ABSTRACT FROM AUTHOR]

We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If p ∈ (0, 1/2) and 1 âˆ' p are the probabilities of occurrence of each Markovian mechanism, then the anomalousness parameter β ∈ (0, 1) results to be β ≃ 1 âˆ' 1/{1 + log[(1 âˆ' p)/ p ]}. Ensemble and single-particle observables of this model have been studied and they match the main characteristics of anomalous diffusion as they are typically measured in living systems. In particular, the celebrated transition of the walker’s distribution from exponential to stretched-exponential and finally to Gaussian distribution is displayed by including also the Brownian yet non-Gaussian interval. [ABSTRACT FROM AUTHOR]

The nature of the first Pop III stars is still a mystery and the energy distribution of the first supernovae is completely unexplored. For the first time we account simultaneously for the unknown initial mass function (IMF), stellar mixing, and energy distribution function (EDF) of Pop III stars in the context of a cosmological model for the formation of a MW-analogue. Our data-calibrated semi-analytic model is based on a N -body simulation and follows the formation and evolution of both Pop III and Pop II/I stars in their proper time-scales. We discover degeneracies between the adopted Pop III unknowns, in the predicted metallicity and carbonicity distribution functions and the fraction of C-enhanced stars. None the less, we are able to provide the first available constraints on the EDF, |$dN/dE_\star \propto E_{\star }^{-\alpha _e}$| with 1 ≤ α e ≤ 2.5. In addition, the characteristic mass of the Pop III IMF should be m ch < 100 M⊙, assuming a mass range consistent with hydrodynamical simulations (0.1–1000 M⊙). Independent of the assumed Pop III properties, we find that all |$\rm [C/Fe]\gt +0.7$| stars (with |$\rm [Fe/H]\lt -2.8$|⁠) have been enriched by Pop III supernovae at a |$\gt 20~{{\ \rm per\ cent}}$| level, and all |$\rm [C/Fe]\gt +2$| stars at a |$\gt 95~{{\ \rm per\ cent}}$| level. All very metal-poor stars with |$\rm [C/Fe]\lt 0$| are predicted to be predominantly enriched by Pop III hypernovae and/or pair instability supernovae. To better constrain the primordial EDF, it is absolutely crucial to have a complete and accurate determination of the metallicity distribution function, and the properties of C-enhanced metal-poor stars (frequency and [C/Fe]) in the Galactic halo. [ABSTRACT FROM AUTHOR]

An abstract of the article "Placental volume and uterine artery Doppler correlation in first trimester of pregnancy," by T. Stampalija and colleagues is presented.

The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one-dimensional problems it is well known that the front advances as the square root of time. When memory or non-locality are introduced into the system, however, this classic signal may be anomalous; replaced by a power-law advance with a time exponent that differs from n = 1/2. Up to now memory treatments in Stefan problem models have only been able to reproduce sub-diffusive front movements with exponents n < 1/2 and non-local treatments have only been able to reproduce super-diffusive behavior n > 1/2. In the present paper, by using a generalized Caputo fractional derivative operator, we introduce new memory and non-local treatment for Stefan problems. On considering a limit case Stefan problem, related to the melting problem, we are able to show that, this general treatment can not only produce arbitrary power-law in time predictions for the front movement but, in the case of memory treatments, can also produce non-power-law anomalous behaviors. Further, also in the context of the limit problem, we are able to establish an equivalence between non-locality and a space varying conductivity and memory and a time varying conductivity. [ABSTRACT FROM AUTHOR]

An abstract of the article "Increased cardiovascular risk in hypertensive disorders (HD) of placental origin," by T. Stampalija, D. Di Martino, M. Quadrifoglio, G. Pagnini, D. Casati, G. Casu, C. Mastroianni, E. Rosti, V. Signorelli, S. Zullino, and E. Ferrazzi is presented.

An abstract of the article "Hypertensive disorders (HD) of placental and maternal origin: evaluation by applanation tonometry" by T. Stampalija, D. Di Martino, M. Quadrifoglio, G. Pagnini, D. Casati, G. Casu, C. Mastroianni, E. Rosti, V. Signorelli, S. Zullino, and E. Ferrazzi is presented.

An abstract of the article "Pulse wave analysis: evaluation of arterial stiffness in first trimester for prediction of placental and maternal pre-eclampsia (PE)," by D. Di Martino, T. Stampalija, M. Quadrifoglio, G. Pagnini, G. Casu, D. Casati, C. Mastroianni, and E. Rosti is presented.

An abstract of the article "First trimester uterine artery Doppler velocimetry and arterial tonometry," by T. Stampalija and colleagues.