Photometric properties and luminosity function of nearby massive early-type galaxies

We perform photometric analyses for a bright early-type galaxy (ETG) sample with 2949 galaxies ($M_{\rm r}<-22.5$ mag) in the redshift range of 0.05 to 0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo 1. We measure the Petrosian and isophotal magnitudes, as well as the corresponding half-light radius for each galaxy. We find that for brightest galaxies ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal magnitudes to 25 ${\rm mag/arcsec^2}$ and 1\% of the sky brightness are on average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian values, respectively. In the first case the underestimations are caused by overestimations in the sky background by the SDSS PHOTO algorithm, while the latter two are also due to deeper photometry. Similarly, the typical half-light radii ($r_{50}$) measured by the SDSS algorithm are smaller than our measurements. As a result, the bright-end of the $r$-band luminosity function is found to decline more slowly than previous works. Our measured luminosity densities at the bright end are more than one order of magnitude higher than those of Blanton et al. (2003), and the stellar mass densities at $M_{\ast}\sim 5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ are a few tenths and a factor of few higher than those of Bernardi et al. (2010). These results may significantly alleviate the tension in the assembly of massive galaxies between observations and predictions of the hierarchical structure formation model.Comment: 43 pages, 14 figures, version accepted for publication in the Astrophysical Journa

Higher dimensional integrable deformations of the modified KdV equation

The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability. The well-known modified KdV equation is a prototypical example of integrable evolution equations in one spatial dimension. Do there exist integrable analogs of modified KdV equation in higher spatial dimensions? In what follows, we present a positive answer to this question. In particular, rewriting the (1+1)-dimensional integrable modified KdV equation in conservation forms and adding deformation mappings during the process allow one to construct higher dimensional integrable equations. Further, we illustrate this idea with examples from the modified KdV hierarchy, also present the Lax pairs of these higher dimensional integrable evolution equations.Comment: 7 pages, 3 figure

Suppression of GSK-3 activation by M-cadherin protects myoblasts against mitochondria-associated apoptosis during myogenic differentiation

Apoptosis occurs concurrently with differentiation of muscle progenitor cells (MPCs) before they fuse to form myotubes. Dysregulated apoptosis in MPCs contributes to the low regeneration capability in aged muscle and decreases the survival rate of donor cells in stem cell-based therapies for muscular dystrophies. This study investigated the role of the M-cadherin/PI3K/Akt/GSK-3β signaling pathway in regulating apoptosis during differentiation of MPCs. Disruption of M-cadherin-dependent cell–cell adhesion by M-cadherin RNA interference in confluent C2C12 myoblasts sensitized the cells to mitochondria-associated intrinsic apoptosis induced by cell confluence or serum starvation. Further investigation of this pathway revealed that M-cadherin-mediated signaling suppressed GSK-3β activation by enhancing the PI3K/AKT-dependent inhibitory phosphorylation of Ser9 in GSK-3β. Overexpression of wild-type GSK-3β in confluent C2C12 myoblasts exacerbated the apoptosis, whereas chemical inhibition of GSK-3β using TDZD-8, or forced expression of constitutively active Akt (myrAkt), or a kinase-deficient GSK-3β mutant [GSK-3β(K85R)], attenuated apoptosis and rescued the impaired myogenic differentiation that is caused by M-cadherin RNA interference. These data suggest that M-cadherin-mediated signaling prevents acceleration of mitochondria-associated intrinsic apoptosis in MPCs by suppressing GSK-3β activation during myogenic differentiation

Numerical simulation of stress wave interaction in short-delay blasting with a single free surface

It is generally believed that stress wave superposition does occur and plays an important role in cutting blasting with a single free surface, in which explosive columns of several blast holes with short spacing are simultaneously initiated. However, considering the large scatter of pyrotechnic delay detonators that are used in most underground metal mines in China, the existence of stress wave superposition and the influence of this effect on rock fragmentation are questionable. In the present study, the stress wave interaction in short-delay blasting with a single free surface was studied through the use of the LS-DYNA code. Stress waves induced by two blast holes blasting with different delays were compared with the single blast hole case, and the effects of delay time, detonating location and spacing on stress wave superposition were investigated. The numerical results showed that for blast holes with a 1 m spacing, stress wave interaction only occurs when the delay time is 0 ms and does not occur for blasting with delays of more than 1 ms. An increase in the duration of a stress wave via optimizing the detonation location does not improve the stress wave interaction. For a 1 ms delay, stress wave superposition only occurs when the spacing is more than 4 m, which is a rare case in practice. The results indicated that the occurrence of stress wave superposition for blasting with a single free surface is strictly limited to conditions that would be difficult to achieve under the existing delay accuracy of detonators. Therefore, it is unrealistic to improve fragmentation via the stress wave interaction in field blasting. Furthermore, the numerical results of the stress wave interaction also show that there would be a great potential to reduce the hazardous vibrations induced by short-delay blasting by using electronic detonators with better control of delays in an order of several milliseconds

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of $m_F=0$ diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.Comment: 5pages, 4 figure

The electrorheology of suspensions consisting of Na-Fluorohectorite synthetic clay particles in silicon oil

Under application of an electric field greater than a triggering electric field $E_c \sim 0.4$ kV/mm, suspensions obtained by dispersing particles of the synthetic clay fluoro-hectorite in a silicon oil, aggregate into chain- and/or column-like structures parallel to the applied electric field. This micro-structuring results in a transition in the suspensions' rheological behavior, from a Newtonian-like behavior to a shear-thinning rheology with a significant yield stress. This behavior is studied as a function of particle volume fraction and strength of the applied electric field, $E$. The steady shear flow curves are observed to scale onto a master curve with respect to $E$, in a manner similar to what was recently found for suspensions of laponite clay [42]. In the case of Na-fluorohectorite, the corresponding dynamic yield stress is demonstrated to scale with respect to $E$ as a power law with an exponent $\alpha \sim 1.93$, while the static yield stress inferred from constant shear stress tests exhibits a similar behavior with $\alpha \sim 1.58$. The suspensions are also studied in the framework of thixotropic fluids: the bifurcation in the rheology behavior when letting the system flow and evolve under a constant applied shear stress is characterized, and a bifurcation yield stress, estimated as the applied shear stress at which viscosity bifurcation occurs, is measured to scale as $E^\alpha$ with $\alpha \sim 0.5$ to 0.6. All measured yield stresses increase with the particle fraction $\Phi$ of the suspension. For the static yield stress, a scaling law $\Phi^\beta$, with $\beta = 0.54$, is found. The results are found to be reasonably consistent with each other. Their similarities with-, and discrepancies to- results obtained on laponite-oil suspensions are discussed

The Error Estimates of the Interpolating Element-Free Galerkin Method for Two-Point Boundary Value Problems

The interpolating moving least-squares (IMLS) method is discussed in detail, and a simpler formula of the shape function of the IMLS method is obtained. Then, based on the IMLS method and the Galerkin weak form, an interpolating element-free Galerkin (IEFG) method for two-point boundary value problems is presented. The IEFG method has high computing speed and precision. Then error analysis of the IEFG method for two-point boundary value problems is presented. The convergence rates of the numerical solution and its derivatives of the IEFG method are presented. The theories show that, if the original solution is sufficiently smooth and the order of the basis functions is big enough, the solution of the IEFG method and its derivatives are convergent to the exact solutions in terms of the maximum radius of the domains of influence of nodes. For the purpose of demonstration, two selected numerical examples are given to confirm the theories