Synthetic horizontal branch morphology for different metallicities and ages under tidally enhanced stellar wind

It is believed that, except for metallicity, some other parameters are needed to explain the horizontal branch (HB) morphology of globular clusters (GCs). Furthermore, these parameters are considered to be correlated with the mass loss of the red giant branch (RGB) stars. In our previous work, we proposed that tidally enhanced stellar wind during binary evolution may affect the HB morphology by enhancing the mass loss of the red giant primary. As a further study, we now investigate the effects of metallicity and age on HB morphology by considering tidally enhanced stellar winds during binary evolution. We incorporated the tidally enhanced-stellar-wind model into Eggleton's stellar evolution code to study the binary evolution. To study the effects of metallicity and age on our final results, we conducted two sets of model calculations: (i) for a fixed age, we used three metallicities, namely Z=0.0001, 0.001, and 0.02. (ii) For a fixed metallicity, Z=0.001, we used five ages in our model calculations: 14, 13, 12, 10, and 7 Gyr. We found that HB morphology of GCs becomes bluer with decreasing metallicity, and old GCs present bluer HB morphology than young ones. These results are consistent with previous work. Although the envelope-mass distributions of zero-age HB stars produced by tidally enhanced stellar wind are similar for different metallicities, the synthetic HB under tidally enhanced stellar wind for Z=0.02 presented a distinct gap between red and blue HB. However, this feature was not seen clearly in the synthetic HB for Z=0.001 and 0.0001. We also found that higher binary fractions may make HB morphology become bluer, and we discussed the results with recent observations.Comment: 16 pages, 6 figures, 3 tables, accepted for publication in Astronomy & Astrophysic

Minimum Wage and Compliance in a Model of Search On-the-Job

minimum wages, compliance, job search, wage growth

An Earthworm-Inspired Soft Crawling Robot Controlled by Friction

We present the modeling, design, fabrication and feedback control of an earthworm-inspired soft robot capable of crawling on surfaces by actively manipulating the frictional force between its body and the surface. Earthworms are segmented worms composed of repeating units known as metameres. The muscle and setae structure embedded in each individual metamere makes possible its peristaltic locomotion both under and above ground. Here, we propose a pneumatically-driven soft robotic system made of parts analogous to the muscle and setae structure and can replicate the crawling motion of a single earthworm metamere. A model is also introduced to describe the crawling dynamics of the proposed robotic system and proven be controllable. Robust crawling locomotion is then experimentally verified.Comment: 8 pages, 9 figures, 1 tabl

A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

A new tow-parameter integrable model of strongly correlated electrons with quantum superalgebra symmetry

A new two-parameter integrable model with quantum superalgebra $U_q[gl(3|1)]$ symmetry is proposed, which is an eight-state electron model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. The model is solved and the Bethe ansatz equations are obtained.Comment: 6 pages, RevTe