Rm Tot Research Articles

LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE

Bearing in mind the application to core-collapse supernovae, we study nonlinear properties of the magneto-rotational instability (MRI) by means of three- dimensional simulations in the framework of a local shearing box approximation. By changing systematically the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear- vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress ($<< w_{\rm tot}>>$) and the shear- vorticity ratio ($g_q$) as $<<w_{\rm tot}>> \propto g_q^{\delta}$ with its index $\delta \sim 0.5$. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has slightly smaller power-law index ($\sim 0.36$). By modeling the effect of viscous heating rates due to the MRI turbulence, we show that the stronger magnetic fields or the larger shear rates initially imposed lead to the higher dissipation rates. For a rapidly rotating PNS with the spin period in milliseconds and with strong magnetic fields of $10^{15}$ G, the energy dissipation rate is estimated to exceed $10^{51} {\rm erg\ sec^{-1}}$. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by the MRI-driven turbulence, which we speculate, on one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface, on the other hand the energy deposition there might be potentially favorable for the working of the neutrino-heating mechanism.

New experimental evidence that the proton develops asymptotically into a black disk

Recently, the Auger group has extracted the proton-air cross section from observations of air showers produced by cosmic ray protons (and nuclei) interacting in the atmosphere and converted it into measurements of the total and inelastic $pp$ cross sections $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ at the super-LHC energy of 57 TeV. Their results reinforce our earlier conclusions that the proton becomes a black disk at asymptotic energies, a prediction reached on the basis of sub-LHC $\pbar p$ and $pp$ measurements of $\sigma_{\rm tot}$ and $\rho$, the ratio of the real to the imaginary part of the forward scattering amplitude [M. M. Block and F. Halzen, Phys. Rev. Lett. {\bf 107}, 212002 (2011)]. The same black disk description of the proton anticipated the values of $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ measured by the TOTEM experiment at the LHC cms (center of mass) energy of $\sqrt s=7$ TeV, as well as those of $\sigma_{\rm inel}$ measured by ALICE, ATLAS and CMS, as well as the ALICE measurement at 2.76 TeV. All data are consistent with a proton that is asymptotically a black disk of gluons: (i) both $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ behave as $\ln^2s$, saturating the Froissart bound, (ii) the forward scattering amplitude becomes pure imaginary (iii) the ratio $\sigma_{\rm inel}/\sigma_{\rm tot}=0.509 \pm 0.021$, compatible with the black disk value of 1/2, and (iv) proton interactions become flavor blind.

Bead‐spring models of entangled polymer melts: Comparison of hard‐core and soft‐core potentials

AbstractTwo bead‐spring models of flexible chains for generic coarse graining of entangled polymer melts, the excluded volume Kremer–Grest (KG) model and the modified segmental repulsive potential (mSRP) combined with a weakly repulsive potential, are compared. For chains containing an equivalent number of entanglements, we compare the chain characteristics of the KG and mSRP polymer models by determining the ratios of the entanglement lengths $ N_{\rm e}^{{\rm KG}} /N_{\rm e}^{{\rm mSRP}} $, the required total number of particles to capture comparable entanglement phenomena $ N_{{\rm tot}}^{{\rm KG}} /N_{{\rm tot}}^{{\rm mSRP}} $, and the time scaling ratios τmSRP/τKG. Our findings show that systems using the mSRP polymer model require half the number of particles and relax four times faster compared to the KG polymer model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012

Antiferromagnetic order in systems with doubletStot=12ground states

We use projector Quantum Monte-Carlo methods to study the $S_{\rm tot}=1/2$ doublet ground states of two dimensional $S=1/2$ antiferromagnets on a $L \times L$ square lattice with an odd number of sites $N_{\rm tot}=L^2$. We compute the ground state spin texture $\Phi^z(\vec{r}) = <S^z(\vec{r})>_{\uparrow}$ in $|G>_{\uparrow}$, the $S^z_{\rm tot}=1/2$ component of this doublet, and investigate the relationship between $n^z$, the thermodynamic limit of the staggered component of this ground state spin texture, and $m$, the thermodynamic limit of the magnitude of the staggered magnetization vector of the same system in the singlet ground state that obtains for even $N_{\rm tot}$. We find a univeral relationship between the two, that is independent of the microscopic details of the lattice level Hamiltonian and can be well approximated by a polynomial interpolation formula: $n^z \approx (1/3 - \frac{a}{2} -\frac{b}{4}) m + am^2+bm^3$, with $a \approx 0.288$ and $b\approx -0.306$. We also find that the full spin texture $\Phi^z(\vec{r})$ is itself dominated by Fourier modes near the antiferromagnetic wavevector in a universal way. On the analytical side, we explore this question using spin-wave theory, a simple mean field model written in terms of the total spin of each sublattice, and a rotor model for the dynamics of $\vec{n}$. We find that spin-wave theory reproduces this universality of $\Phi^z(\vec{r})$ and gives $n^z = (1-\alpha -\beta/S)m + (\alpha/S)m^2 +{\mathcal O}(S^{-2})$ with $\alpha \approx 0.013$ and $\beta \approx 1.003$ for spin-$S$ antiferromagnets, while the sublattice-spin mean field theory and the rotor model both give $n^z = 1/3 m$ for $S=1/2$ antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range {\em unfrustrated} exchange interactions.

Total hadronic cross sections andπ∓π+scattering

Recent measurements of the inelastic and total proton-proton cross section at the LHC, and at cosmic ray energies by the Auger experiment, have quantitatively confirmed fits to lower energy data constrained by the assumption that the proton is asymptotically a black disk of gluons. We show that data on \bar p(p)p,\pi^\mp p, and K^\mp p forward scattering support the related expectation that the asymptotic behavior of all cross sections is flavor independent. By using the most recent measurements from ATLAS, CMS, TOTEM and Auger, we predict \sigma^{pp}_{\rm tot} (\sqrt s=8 {\rm TeV})=100.6 \pm 2.9 mb and \sigma^{pp}_{\rm tot} (\sqrt s=14 {\rm TeV})=110.8 \pm 3.5 mb, as well as refine the total cross section \sigma^{pp}_{\rm tot} (\sqrt s=57 {\rm TeV})=139.6 \pm 5.4 mb. Our analysis also predicts the total \pi^\mp \pi^+ cross sections as a function of \sqrt s.

The evolution of embedded star clusters

We study the evolution of embedded clusters. The equations of motion of the stars in the cluster are solved by direct N-body integration while taking the effects of stellar evolution and the hydrodynamics of the natal gas content into account. The gravity of the stars and the surrounding gas are coupled self consistently to allow the realistic dynamical evolution of the cluster. While the equations of motion are solved, a stellar evolution code keeps track of the changes in stellar mass, luminosity and radius. The gas liberated by the stellar winds and supernovae deposits mass and energy into the gas reservoir in which the cluster is embedded. We examine cluster models with 1000 stars, but we varied the star formation efficiency (between 0.05-0.5), cluster radius (0.1-1.0 parsec), the degree of virial support of the initial population of stars (0-100%) and the strength of the feedback. We find that an initial star fraction $M_\star/M_{\rm tot} > 0.05$ is necessary for cluster survival. Survival is more likely if gas is not blown out violently by a supernova and if the cluster has time to approach virial equilibrium during out-gassing. While the cluster is embedded, dynamical friction drives early and efficient mass segregation in the cluster. Stars of $m \gtrsim 2\,M_\odot$ are preferentially retained, at the cost of the loss of less massive stars. We conclude that the degree of mass segregation in open clusters such as the Pleiades is not the result of secular evolution but a remnant of its embedded stage.

Ultrahigh energy predictions of proton-air cross sections from accelerator data: An update

At $\sqrt s = 57\pm 7$ TeV, the Pierre Auger Observatory (PAO) collaboration has recently measured the proton-air inelastic production cross section $\sigma_{\rm p-air}$. Assuming a helium contamination of 25%, they subtracted 30 mb from their measured value, resulting in a p-air inelastic production cross section, $\sigma_{\rm p-air}=475 \pm 22\ ({\rm stat.})\pm^{20}_{15} \ ({\rm syst.})$ mb, exclusive of helium contamination. Using this result in a Glauber calculation to obtain the $pp$ inelastic cross section, they found the inelastic $pp$ cross section $\sigma_{\rm inel}= 90\pm 7\ ({\rm stat.}) \pm^9_{11} ({\rm syst.}) \pm 1.5 {\rm \ (Glaub.})$ mb. Parameterization of the $\bar pp$ and $pp$ cross sections incorporating analyticity constraints and unitarity has allowed us to make accurate extrapolations to ultra-high energies, and using Glauber calculations, accurately predict cosmic ray results for $\spai$. In this update for 57 TeV, we predict i) a $pp$ total cross section, $\sigma_{\rm tot}=133.4\pm 1.6$ mb, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar pp$ and $pp$ scattering amplitudes and ii) a p-air inelastic production cross section, $\sigma_{\rm p-air}=483\pm 3 $ mb, by using $\sigma_{\rm tot}$ together with Glauber theory, allowing us to determine independently that the helium contamination was 19%, in reasonable agreement with their estimate of 25%. Our predictions agree with all available cosmic ray extensive air shower measurements, both in magnitude and in energy dependence. By using our value for the $pp$ total cross section at 57 TeV, Block and Halzen \cite{blackdisk} have predicted that the $pp$ inelastic cross section is $\sigma_{\rm inel}= 92.9\pm 1.6$ mb, in agreement with the measured POA value.

Interacting ghost dark energy in non-flat universe

A new dark energy model called "ghost dark energy" was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, $\rho_D=\alpha H$, where $\alpha$ is a constant of order $\Lambda_{\rm QCD}^3$ and $\Lambda_{\rm QCD}\sim 100 MeV$ is QCD mass scale. In this paper, we extend the ghost dark energy model to the universe with spatial curvature in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail. In the absence of interaction the equation of state parameter of ghost dark energy is always $w_D > -1 $ and mimics a cosmological constant in the late time, while it is possible to have $w_D < -1 $ provided the interaction is taken into account. When $k = 0$, all previous results of ghost dark energy in flat universe are recovered. To check the observational consistency, we use Supernova type Ia (SNIa) Gold sample, shift parameter of Cosmic Microwave Background radiation (CMB) and the Baryonic Acoustic Oscillation peak from Sloan Digital Sky Survey (SDSS). The best fit values of free parameter at $1\sigma$ confidence interval are: $\Omega_m^0= 0.35^{+0.02}_{-0.03}$, $\Omega_D^0=0.75_{-0.04}^{+0.01}$ and $b^2=0.08^{+0.03}_{-0.03}$. Consequently the total energy density of universe at present time in this model at 68% level equates to $\Omega_{\rm tot}^0=1.10^{+0.02}_{-0.05}$.

SUNYAEV–ZEL'DOVICH SCALING RELATIONS FROM A SIMPLE PHENOMENOLOGICAL MODEL FOR GALAXY CLUSTERS

We build a simple, {\it top-down} model for the gas density and temperature profiles for galaxy clusters. The gas is assumed to be in hydrostatic equilibrium along with a component of non-thermal pressure taken from simulations and the gas fraction approaches the cosmic mean value only at the virial radius or beyond. The free parameters of the model are the slope and normalisation of the concentration-mass relation, the gas polytropic index, and slope and normalisation of the mass-temperature relation. These parameters can be fixed from X-Ray and lensing observations. We compare our gas pressure profiles to the recently proposed `Universal' pressure profile by \cite{Arnaud09} and find very good agreement. We find that the Sunyaev-Zel'dovich Effect (SZE) scaling relations between the integrated SZE flux, $Y$, the cluster gas temperature, $T_{\rm sl}$, the cluster mass, $M_{\rm tot}$, and the gas mass, $M_{\rm gas}$ are in excellent agreement with the recently observed $r_{2500}$ SZE scaling relations by \cite{Bonamente08} and $r_{500}$ relation by \cite{Arnaud09}. The gas mass fraction increases with cluster mass and is given by $f_{\rm gas}(r_{500}) = 0.1324 + 0.0284 \,\rm{log}\, (\frac{M_{500}}{10^{15}h^{-1}M_\odot})$. This is within $10%$ of observed $f_{\rm gas}(r_{500})$. The consistency between the global properties of clusters detected in X-Rays and in SZE shows that we are looking at a common population of clusters as a whole, and there is no deficit of SZE flux relative to expectations from \xr scaling properties. Thus, it makes it easier to compare and cross-calibrate clusters from upcoming \xr and SZE surveys.

THE SL2S GALAXY-SCALE LENS SAMPLE. II. COSMIC EVOLUTION OF DARK AND LUMINOUS MASS IN EARLY-TYPE GALAXIES

We present a joint gravitational lensing and stellar-dynamical analysis of 11 early-type galaxies (median deflector redshift $\zd=0.5$) from Strong Lenses in the Legacy Survey (SL2S). Using newly measured redshifts and stellar velocity dispersions from Keck spectroscopy with lens models from Paper I, we derive the total mass density slope inside the Einstein radius for each of the 11 lenses. The average total density slope is found to be $<\gamma'>= 2.16^{+0.09}_{-0.09}$ ($\rho_{\rm tot}\propto r^{-\gamma'}$), with an intrinsic scatter of $0.25^{+0.10}_{-0.07}$. We also determine the dark matter fraction for each lens within half the effective radius, and find the average projected dark matter mass fraction to be $0.42^{+0.08}_{-0.08}$ with a scatter of $0.20^{+0.09}_{-0.07}$ for a Salpeter IMF. By combining the SL2S results with those from the Sloan Lens ACS Survey (median $\zd=0.2$) and the Lenses Structure and Dynamics survey (median $\zd=0.8$), we investigate cosmic evolution of $\gamma'$ and find a mild trend $\partial<\gamma'>/\partial\zd = -0.25^{+0.10}_{-0.12}$. This suggests that the total density profile of massive galaxies has become slightly steeper over cosmic time. If this result is confirmed by larger samples, it would indicate that dissipative processes played some role in the growth of massive galaxies since $z\sim1$.

A closed-form solution to the minimum $${\Delta V_{\rm tot}^2}$$ Lambert’s problem

A closed form solution to the minimum \({\Delta V_{\rm tot}^2}\) Lambert problem between two assigned positions in two distinct orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices to solve re-configuration problems of satellite constellations and the complexity associated in facing these problems with the minimization of \({\Delta V_{\rm tot}}\). Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing \({\Delta V_{\rm tot}^2}\) and \({\Delta V_{\rm tot}}\) does not exceed 17%. The \({\Delta V_{\rm tot}^2}\) solution can be adopted as starting point to find the minimum \({\Delta V_{\rm tot}}\). The solving equation for minimum \({\Delta V_{\rm tot}^2}\) Lambert problem is a quartic polynomial in term of the angular momentum modulus of the optimal transfer orbit. The root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. A numerical example for the general case (orbit transfer “pork-chop” between two non-coplanar elliptical orbits) and two examples for the singular case (Hohmann and GTO transfers) are provided.

Measurement of the isospin-filtering dd $ \rightarrow$ 4HeK+K- reaction at Q = 39 MeV

The total cross-section for the dd $ \rightarrow$ 4HeK + K - reaction has been measured at a beam momentum of 3.7GeV/c, corresponding to an excess energy of 39MeV, which is the maximum possible at the Cooler Synchrotron COSY-Julich. A deuterium cluster-jet target and the ANKE forward magnetic spectrometer, placed inside the storage ring, have been employed in this investigation. We find a total cross-section of $ \sigma_{{{\rm tot}}}^{}$ < 14 pb, which brings into question the viability of investigating the dd $ \rightarrow$ 4Hea 0(980) reaction as a means of studying isospin violation.

A Satellite Approach to Estimate Land–Atmosphere $\hbox{CO}_{2}$ Exchange for Boreal and Arctic Biomes Using MODIS and AMSR-E

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Northern ecosystems are a major sink for atmospheric <formula formulatype="inline"><tex Notation="TeX">$\hbox{CO}_{2}$</tex> </formula> and contain much of the world's soil organic carbon (SOC) that is potentially reactive to near-term climate change. We introduce a simple terrestrial carbon flux (TCF) model driven by satellite remote sensing inputs from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) to estimate surface (<formula formulatype="inline"><tex Notation="TeX">$≪ 10$</tex></formula>-cm depth) SOC stocks, daily respiration, and net ecosystem carbon exchange (NEE). Soil temperature and moisture information from AMSR-E provide environmental constraints to soil heterotrophic respiration <formula formulatype="inline"><tex Notation="TeX">$(R_{h})$ </tex></formula>, while gross primary production (GPP) information from MODIS provides estimates of the total photosynthesis and autotrophic respiration. The model results were evaluated across a North American network of boreal forest, grassland, and tundra monitoring sites using alternative carbon measures derived from tower <formula formulatype="inline"><tex Notation="TeX">$\hbox{CO}_{2}$</tex></formula> flux measurements and BIOME-BGC model simulations. Root-mean-square-error (rmse) differences between TCF model estimates and tower observations were 1.2, 0.7, and 1.2 <formula formulatype="inline"><tex Notation="TeX">$\hbox{g} \cdot \hbox{C} \cdot \hbox{m}^{-2} \cdot \hbox{day}^{-1}$ </tex></formula> for GPP, ecosystem respiration <formula formulatype="inline"><tex Notation="TeX">$({\rm R}_{\rm tot})$</tex> </formula> and NEE, while mean residual differences were 43% of the rmse. Similar accuracies were observed for both TCF and BIOME-BGC model simulations relative to tower results. TCF-model-derived SOC was in general agreement with soil inventory data and indicates that the dominant SOC source for <formula formulatype="inline"><tex Notation="TeX">$R_{h}$</tex> </formula> has a mean residence time of less than five years, while <formula formulatype="inline"><tex Notation="TeX">$R_{h}$</tex> </formula> is approximately 43% and 55% of <formula formulatype="inline"><tex Notation="TeX">$R_{\rm tot}$</tex></formula> for respective summer and annual fluxes. An error sensitivity analysis determined that meaningful flux estimates could be derived under prevailing climatic conditions at the study locations, given documented error levels in the remote sensing inputs. </para>

MOLECULAR HYDROGEN IN THE FAR ULTRAVIOLET SPECTROSCOPIC EXPLORER TRANSLUCENT LINES OF SIGHT: THE FULL SAMPLE

We report total abundances and related parameters for the full sample of the FUSE survey of molecular hydrogen in 38 translucent lines of sight. New results are presented for the "second half" of the survey involving 15 lines of sight to supplement data for the first 23 lines of sight already published. We assess the correlations between molecular hydrogen and various extinction parameters in the full sample, which covers a broader range of conditions than the initial sample. In particular, we are now able to confirm that many, but not all, lines of sight with shallow far-UV extinction curves and large values of the total-to-selective extinction ratio, $R_V$ = $A_V$ / $E(B-V)$ -- characteristic of larger than average dust grains -- are associated with particularly low hydrogen molecular fractions ($f_{\rm H2}$). In the lines of sight with large $R_V$, there is in fact a wide range in molecular fractions, despite the expectation that the larger grains should lead to less H$_2$ formation. However, we see specific evidence that the molecular fractions in this sub-sample are inversely related to the estimated strength of the UV radiation field and thus the latter factor is more important in this regime. We have provided an update to previous values of the gas-to-dust ratio, $N$(H$_{\rm tot}$)/$E(B-V)$, based on direct measurements of $N$(H$_2$) and $N$(H I). Although our value is nearly identical to that found with Copernicus data, it extends the relationship by a factor of 2 in reddening. Finally, as the new lines of sight generally show low to moderate molecular fractions, we still find little evidence for single monolithic "translucent clouds" with $f_{\rm H2}$ $\sim$ 1.

Efficient Analysis of Phased Arrays of Microstrip Patches Using a Hybrid Generalized Forward Backward Method/Green's Function Technique With a DFT Based Acceleration Algorithm

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficients corresponding to a single patch are first solved by a conventional Galerkin type hybrid method of moments (MoM)/Green's function technique that uses the grounded dielectric slab's Green's function. Because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions, the patch can have any shape. The solution for the array currents is then found through GFBM, where it sweeps the current computation element by element. The computational complexity of this method, which is originally <formula formulatype="inline"><tex>$O\left(N_{\rm tot}^{2}\right)$</tex> </formula> (<formula formulatype="inline"><tex>$N_{\rm tot}$</tex></formula> being the total number of unknowns) for each iteration, is reduced to <formula formulatype="inline"> <tex>$O(N_{\rm tot})$</tex></formula> using a DFT based acceleration algorithm making use of the fact that array elements are identical and the array is periodic. Numerical results in the form of array current distribution are given for various sized arrays of probe-fed microstrip patches with elliptical and/or circular boundaries, and are compared with the conventional MoM results to illustrate the efficiency and accuracy of the method. </para>

Aggregate packing and -void saturation in mortar and concrete proportioning

Proportioning was studied by measuring aggregate packing (C) and filling of aggregate void space (1−C) with varying volumes of cement paste (\(V_{\rm p}\)) or matrix (\(V_{\rm matrix}\)), i.e., all material <0.125 mm. Eleven widely different normal density aggregates with C = 0.57 to 0.71, i.e., aggregate void content (1−C) = 0.29 to 0.43, were used at constant w/c = 0.38 and flowing consistency and varying dosage of water reducer and paste- and matrix volume. Analysing plots of four excess phase volumes (paste with/without air, matrix with/without air) versus aggregate void space showed constant aggregate void saturation ratios. Both paste- and matrix-aggregate void saturation ratio can be used with the best estimate (\(V_{\rm p}-V_{\rm air})/{(1-C)}=1.15\) per \(\hbox{m}^{3}\). Including air voids in paste- or matrix volume improved correlation so air void content must be included in the normalized paste aggregate void saturation ratio (\(k=V_{\rm p}\)/[(1−C) \(V_{\rm tot}\)]). Simple measurements of aggregate packing are thus very useful. Cost per unit material, per unit fresh (slump, flow diameter) or hardened (compressive strength) property were used to show the cost efficiency of the mixes. The ranking of cost/MPa strength and cost/mm consistency is similar to ranking of total concrete cost for the 11 aggregates with a certain scatter though.

Adaptive smoothing lengths in SPH

Context: There is a need to improve the fidelity of SPH simulations of self-gravitating gas dynamics. Aims: We remind users of SPH that, if smoothing lengths are adjusted so as to keep the number of neighbours, ${\cal N}$, in the range ${\cal N}_{_{\rm NEIB}}\pm\Delta{\cal N}_{_{\rm NEIB}}$, the tolerance, $\Delta{\cal N}_{_{\rm NEIB}}$, should be set to zero, as first noted by Nelson & Papaloizou. We point out that this is a very straightforward and computationally inexpensive constraint to implement. Methods: We demonstrate this by simulating acoustic oscillations of a self-gravitating isentropic monatomic gas-sphere (cf. Lucy), using ${\cal N}_{_{\rm TOT}}\sim6,000$ particles and ${\cal N}_{_{\rm NEIB}}=50$. Results: We show that there is a marked reduction in the rates of numerical dissipation and diffusion as $\Delta{\cal N}_{_{\rm NEIB}}$ is reduced from 10 to zero. Moreover this reduction incurs a very small computational overhead. Conclusions: We propose that this should become a standard test for codes used in simulating star formation. It is a highly relevant test, because pressure waves generated by the switch from approximate isothermality to approximate adiabaticity play a critical role in the fragmentation of collapsing prestellar cores. Since many SPH simulations in the literature use ${\cal N}_{_{\rm NEIB}}=50$ and $\Delta{\cal N}_{_{\rm NEIB}}\geq10$, their results must be viewed with caution.

Monte Carlo simulations of metal-poor star clusters

Context. Metal-poor globular clusters (GCs) can provide a probe of the earliest epoch of star formation in the Universe, being the oldest observable stellar systems. In addition, young and intermediate-age low-metallicity GCs are present in external galaxies. Nevertheless, inferring their evolutionary status by using integrated properties may suffer from large intrinsic uncertainty caused by the discrete nature of stars in stellar systems, especially in the case of faint objects. Aims. In this paper, we evaluate the intrinsic uncertainty (due to statistical effects) affecting the integrated colours and mass-to-light ratios as a function of the cluster's integrated visual magnitude ($M_V^{\rm tot}$), which represents a directly measured quantity. We investigate the case of metal-poor, single-burst stellar populations with age from a few million years to a likely upper value for the Galactic globular cluster ages (~15 Gyr). Methods. Our approach is based on Monte Carlo techniques for randomly generating stars distributed according to the cluster's mass function. Results. Integrated colours and mass-to-light ratios in different photometric bands are checked for good agreement with the observational values of low-metallicity Galactic clusters; the effect of different assumptions on the horizontal branch (HB) morphology is shown to be irrelevant, at least for the photometric bands explored here. We present integrated colours and mass-to-light ratios as a function of age for different assumptions on the cluster total V magnitude. We find that the intrinsic uncertainty cannot be neglected. In particular, in models with $M_V^{\rm tot}=-4$ the broad-band colours show an intrinsic uncertainty high enough to prevent the precise age of the cluster from being evaluated. The effects of different assumptions on the initial mass function and on the minimum mass for which carbon burning is ignited for both integrated colours and mass-to-light ratios are also analysed. Finally, the present predictions are compared with recent results available in the literature, showing non-negligible differences in some cases.

Non-equilibrium beta processes in neutron stars: a relationship between the net reaction rate and the total emissivity of neutrinos

Several different processes could be changing the density in the core of a neutron star, leading to a departure from $\beta$ equilibrium, quantified by the chemical potential difference $\delta\mu\equiv\mu_n-\mu_p-\mu_e$. The evolution of this quantity is coupled to that of the star's interior temperature $T$ by two functions that quantify the rate at which neutrino-emitting reactions proceed: the net reaction rate (difference between $\beta$ decay and capture rates), $\Gamma_{\rm net}(T,\delta\mu)$, and the total emissivity (total energy emission rate in the form of neutrinos and antineutrinos), $\epsilon_{\rm tot}(T,\delta\mu)$. Here, we present a simple and general relationship between these variables, ${\partial\epsilon_{\rm tot}/\partial\delta\mu=3\Gamma_{\rm net}}$, and show that it holds even in the case of superfluid nucleons. This relation may simplify the numerical calculation of these quantities, including superfluid reduction factors.

Magnetoresistance and spin polarization in the insulating regime of a Si two-dimensional electron system

We have studied the magnetoresistance in a high-mobility Si inversion layer down to low electron concentrations at which the longitudinal resistivity $\rho_{xx}$ has an activated temperature dependence. The angle of the magnetic field was controlled so as to study the orbital effect proportional to the perpendicular component $B_\perp$ for various total strengths $B_{\rm tot}$. A dip in $\rho_{xx}$, which corresponds to the Landau level filling factor of $\nu=4$, survives even for high resistivity of $\rho_{xx} \sim 10^8 \Omega$ at $T= 150 {\rm mK}$. The linear $B_{\rm tot}$-dependence of the value of $B_\perp$ at the dip for low $B_{\rm tot}$ indicates that a ferromagnetic instability does not occur even in the far insulating regime.