Compression of an elastic roller between two rigid plates

A closed solution - exact within two-dimensional linear elastostatics - is deduced for the problem appropriate to the compression of an elastic circular cylinder between two smooth, flat and parallel, rigid plates. The boundary displacements obtained for the cylinder involve elliptic integrals, whereas its stress field is given in terms of elementary functions exclusively. The results found for the distribution of the contact pressure and for the width of the contact zone are compared with the corresponding predictions of Hertz's approximate theory, for which elementary corrections are determined by asymptotic means. Analogous corrections are established for a previously available approximate estimate of the diametral compression undergone by the roller, which remains indeterminate in the Hertz treatment of this two-dimensional contact problem

Inflating Fat Bubbles in Clusters of Galaxies by Precessing Massive Slow Jets

We conduct hydrodynamical numerical simulations and find that precessing massive slow jets can inflate fat bubbles, i.e., more or less spherical bubbles, that are attached to the center of clusters of galaxies. To inflate a fat bubble the jet should precess fast. The precessing angle $\theta$ should be large, or change over a large range $0 \le \theta \le \theta_{\max} \sim 30-70 ^\circ$ (depending also on other parameters), where $\theta=0$ is the symmetry axis. The constraints on the velocity and mass outflow rate are similar to those on wide jets to inflate fat bubbles. The velocity should be v_j \sim 10^4 \kms, and the mass loss rate of the two jets should be 2 \dot M_j \simeq 1-50 \dot M_\odot \yr^{-1} . These results, and our results from a previous paper dealing with slow wide jets, support the claim that a large fraction of the feedback heating in cooling flow clusters and in the processes of galaxy formation is done by slow massive jets.Comment: Accepted for publication in MNRA

The no-core shell model with general radial bases

Calculations in the ab initio no-core shell model (NCSM) have conventionally been carried out using the harmonic-oscillator many-body basis. However, the rapid falloff (Gaussian asymptotics) of the oscillator functions at large radius makes them poorly suited for the description of the asymptotic properties of the nuclear wavefunction. We establish the foundations for carrying out no-core configuration interaction (NCCI) calculations using a basis built from general radial functions and discuss some of the considerations which enter into using such a basis. In particular, we consider the Coulomb-Sturmian basis, which provides a complete set of functions with a realistic (exponential) radial falloff.Comment: 7 pages, 3 figures; presented at Horizons on Innovative Theories, Experiments, and Supercomputing in Nuclear Physics 2012, New Orleans, Louisiana, June 4-7, 2012; submitted to J. Phys. Conf. Se

Near-Infrared Microlensing of Stars by the Super-Massive Black Hole in the Galactic Center

We investigate microlensing amplification of faint stars in the dense stellar cluster in the Galactic Center (GC) by the super-massive black hole (BH). Such events would appear very close to the position of the radio source SgrA*, which is thought to coincide with the BH, and could be observed during the monitoring of stellar motions in the GC. We use the observed K-band (2.2 um) luminosity function (KLF) in the GC and in Baade's Window, as well as stellar population synthesis computations, to construct KLF models for the inner 300 pc of the Galaxy. These, and the observed dynamical properties of this region, are used to compute the rates of microlensing events, which amplify stars above specified detection thresholds. We present computations of the lensing rates and amplifications as functions of the event durations (weeks to years), for a range of detection thresholds. We find that short events dominate the total rate and that long events tend to have large amplifications. For the current detection limit of K=17 mag, the total microlensing rate is 0.003 1/yr, and the rate of events with durations >1 yr is 0.001 1/yr. Recent GC proper motion studies have revealed the possible presence of one or two variable K-band sources very close to SgrA* (Genzel et al 97; Ghez et al 98). These sources may have attained peak brightnesses of K~15 mag, about 1.5-2 mag above the observational detection limits, and appear to have varied on a timescale of ~1 yr. This behavior is consistent with long-duration microlensing of faint stars by the BH. However, we estimate that the probability that such an event could have been detected during the course of the recent proper motion studies is \~0.5%. A ten-fold improvement in the detection limit and 10 yr of monthly monitoring would increase the total detection probability to ~20%. (Abridged)Comment: 29 p. with 5 figs. To appear in ApJ. Changed to reflect published version. Short discussions of solar metallicity luminosity function and star-star microlensing adde

Seeing beyond negotiations: the impacts of the Belt and Road on Sino-Kazakh transboundary water management

China’s Belt and Road Initiative (BRI) and infrastructural development has led to growing concerns regarding the future of Central Asia’s water resources. However, few attempts have been made to assess the impacts this will have on specific transboundary basins within the region. This article explores how the context of the BRI transcends its physical impacts within the Ili and Irtysh basins, creating a sanctioned discourse that forecloses the possibility of ‘successful’ negotiations at an official level. As such, pathways to transboundary water management that exist beyond the negotiations are shown to have greater plausibility and potential effectiveness.info:eu-repo/semantics/publishedVersio

The Initial Mass Functions in the Super-Star-Clusters NGC 1569A and NGC 1705-1

I use recent photometric and stellar velocity dispersion measurements of the super-star-clusters (SSCs) NGC 1569A and NGC 1705-1 to determine their present-day luminosity/mass (L_V/M) ratios. I then use the inferred L_V/M ratios, together with population synthesis models of evolving star-clusters, to constrain the initial-mass-functions (IMFs) in these objects. I find that (L_V/M)_solar=28.9 in 1569A, and (L_V/M)_solar=126 in 1705-1. It follows that in 1569A the IMF is steep with alpha~2.5 for m**(-alpha)dm IMFs which extend to 0.1 M_sun. This implies that most of the stellar mass in 1569A is contained in low-mass (< 1 M_sun) stars. However, in 1705-1 the IMF is either flat, with alpha<2$, or it is truncated at a lower mass-limit between 1 and 3 M_sun. I compare the inferred IMFs with the mass functions (MFs) of Galactic globular clusters. It appears that 1569A has a sufficient reservoir of low-mass stars for it to plausibly evolve into an object similar to Galactic globular clusters. However, the apparent deficiency of low-mass stars in 1705-1 may make it difficult for this SSC to become a globular cluster. If low-mass stars do dominate the cluster mass in 1705-1, the large L_V/M ratio in this SSC may be evidence that the most massive stars have formed close to the cluster cores.Comment: ApJ, in press. 19 Pages, Latex; [email protected]

Group projector generalization of dirac-heisenberg model

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is applied to the system of identical particles with spin independent interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space for arbitrary orbital occupation numbers and arbitrary spin. This gives transparent insight into the physical contents of this hamiltonian, showing that formal generalizations with spin greater than 1/2 involve nontrivial additional physical assumptions.Comment: 10 page