Mg^{2 } and bovine
serum albumin (BSA) Langmuir monolayers were used as effective crystal
nucleation, growth modifiers and template to control the crystallization of
CaCO_{3}. Scanning electron microscopy (SEM), and X-ray diffraction
(XRD) were used to characterize the polymorph and morphology of crystals
obtained at different experimental conditions, respectively. The results
indicated that various morphologies such as abacus-bead-like particles,
spherical-shaped particles, wood block-like
particles, pignut-shell-like particles and
the rolling pole shaped particles have been formed at the interface of air-solution. The
polymorph of calcium carbonate obtained undergo an evolvement from calcite to vaterite
and aragonite with increasing of the molar ratio of Mg^{2 } to Ca^{2 },
which indicated that the ability of Mg^{2 } to induce the formation of
aragonite was enhanced as the molar ratio of Mg^{2 } to Ca^{2 } increased. When the molar ratio reached 3, the samples obtained were all
aragonite phase of calcium carbonate, which suggests that the presence of Mg^{2 } of subphase solutions was helpful for the formation of aragonite phase in the
systems of Mg^{2 }-BSA Langmuir monolayers. The possible formation
mechanisms of CaCO_{3} in different systems were discussed in the paper.

The crystallization of calcium carbonate at interface of Langmuir monolayers of bovine serum albumin and subphase containing magnesium ions was studied in this paper. The results were characterized by using powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). The effect rules were obtained by the cooperation of bovine serum albumin Langmuir monolayers and magnesium ions. BSA Langmuir monolayers controlled calcium carbonate to magnesium ions in solution. The experiment results showed that in the presence of both BSA Langmuir monolayers at interface and magnesium ions in solutions, an orientation aragonite with regular spherical morphology was precipitated. It is indicated that BSA Langmuir monolayers and magnesium ions have a cooperative effect on controlling the polymorph and orientation of calcium carbonate crystal. The experiments suggested that BSA Langmuir monolayer acts in combination with magnesium ions to inhibit calcite crystal growth, while favoring the formation of aragonite crystals.

Monolayers of L-α-Dipalmitoylphosphatidylcholine (DPPC) on the air-water interface have been transferred at a middling applied surface-pressure onto the mica substrates using the Langmuir-Blodgett (LB) technique. AFM was applied to observe the formation of morphology of DPPC. Our results show that the Langmuir-Blodgett monolayers of DPPC on mica substrates generate a structured surface with periodic channels and stripes. The LB monolayers obtained at a surface pressure correspond to 20 mN/n. We take into account several explanations to understand the observed surface topological views. On the other hand, a lot of lipids, their Langmuir monolayer and Langmuir-Blodgett monolayer are excellent models of half-layer biological membranes, which can provide closer biological environment. Therefore, using the lipid Langmuir-Blodgett or Langmuir monolayer as prototype, one can simulate further biological environment and make further investigation on biomineralization mechanism of template-controlled.

Abstract:
We provide a sufficient condition for constructing a class of compactly supported refinable functions with componentwise polynomial property in . An iteration algorithm is developed to compute the polynomial on each component of the functions' support. Finally, two examples for constructing the symmetric refinable componentwise polynomial functions are given. 1. Introduction Refinable functions are among the most important functions; they form the foundation of wavelet theory and subdivision scheme theory. The details can be found in [1–3]. Other areas in which refinable functions play important roles are fractal geometry and self-affine tilings (see [4–6]). Splines, as well as refinable functions, have been widely used in numerical solutions of differential and integral equations, digital signal processing, image compression, and many others. Particularly, the refinable splines such as -splines in and the box splines in play a key role in approximation theory and in computer-aided geometric design. In recent years, some researches on refinable splines have made great progress (see [7–15]). As we know, a refinable function with an analytic expression is of great importance, especially in those requiring high-precision domains. However, refinable functions are solutions of refinement equations and are usually defined by some cascade algorithms. Due to the iterative process, most of refinable functions do not have explicit analytic expression. In [9, 11], the authors have proved that there are no other piecewise smooth compactly supported refinable functions with explicit analytic expression than -splines. Then much attention has been given in the literature to the componentwise polynomial since it is a polynomial on each connected component of the function’s support, and there are some preliminary researches on this field (see [16–20]). What is a spline in ? And what is a componentwise polynomial in ? Definition 1.1 (see [7]). A compactly supported function in with supp is called a spline if there exists a partition into simplices in such that is a polynomial on each . Definition 1.2 (see [16]). A compactly supported function is a componentwise polynomial if there exists an open set such that the Lebesgue measure of is zero and the restriction of on any connected open component of coincides with some polynomial. Generally, the componentwise polynomial is not a spline; it is much broader than a spline. The difference between the componentwise polynomial and the spline is that the former’s support consists of infinitely many simplices, and the latter’s is

Abstract:
The gas dynamics in protoplanetary disks (PPDs) is strongly affected by non-ideal MHD effects. Using a complex chemical reaction network with standard prescriptions for X-ray and cosmic-ray ionizations, as well as the most up-to-date results from numerical simulations, we study the non-ideal MHD effects on the magnetorotational instability (MRI) and angular momentum transport in PPDs. We first show that no matter grains are included or not, the recombination time is always shorter than the orbital time in the bulk of PPDs, justifying the validity of local ionization equilibrium. The full conductivity tensor at different disk radii and heights is evaluated, with the MRI active region determined by requiring that (1) the Ohmic Elsasser number be greater than 1; (2) the ratio of gas to magnetic pressure beta be greater than beta_min(Am) as identified by Bai & Stone (2011), where Am is the Elsasser number for ambipolar diffusion. With full flexibility as to the magnetic field strength, we provide a general framework for estimating the MRI-driven accretion rate M_dot and the magnetic field strength in the MRI-active layer. We find that the MRI-active layer always exists at any disk radii as long as the magnetic field in PPDs is sufficiently weak. However, the optimistically predicted M_dot in the inner disk (r=1-10 AU) appears insufficient to account for the observed range of accretion rate in PPDs (around 1e-8M_Sun/yr) even in the grain-free calculation, and the presence of solar abundance sub-micron grains further reduces M_dot by one to two orders of magnitude. Our results suggest that stronger sources of ionization, and/or additional mechanisms such as magnetized wind are needed to explain the observed accretion rates in PPDs. In contrast, our predicted M_dot is on the order of 1e-9M_Sun/yr in the outer disk, consistent with the observed accretion rates in transitional disks. (Abridged)

Abstract:
Tiny grains such as PAHs have been thought to dramatically reduce the coupling between gas and magnetic fields in weakly ionized gas such as in protoplanetary disks (PPDs) because they provide tremendous surface area to recombine free electrons. The presence of tiny grains in PPDs thus raises the question of whether the magnetorotational instability (MRI) is able to drive rapid accretion to be consistent with observations. Charged tiny grains have similar conduction properties as ions, whose presence leads to qualitatively new behaviors in the conductivity tensor, characterized by n_bar/n_e>1, where n_e and n_bar denote the number densities of free electrons and all other charged species respectively. In particular, Ohmic conductivity becomes dominated by charged grains rather than electrons when n_bar/n_e exceeds about 10^3, and Hall and ambipolar diffusion (AD) coefficients are reduced by a factor of (n_bar/n_e)^2 in the AD dominated regime relative to that in the Ohmic regime. Applying the methodology of Bai (2011), we find that in PPDs, when PAHs are sufficiently abundant (>1e-9 per H_2), there exists a transition radius r_trans of about 10-20 AU, beyond which the MRI active layer extends to the disk midplane. At rr_trans, we find that remarkably, the predicted M_dot exceeds the grain-free case due to a net reduction of AD by charged tiny grains, and reaches a few times 1e-8M_Sun/yr. This is sufficient to account for the observed M_dot in transitional disks. Larger grains (>0.1 micron) are too massive to reach such high abundance as tiny grains and to facilitate the accretion process.

Abstract:
Non-ideal magnetohydrodynamical effects play a crucial role in determining the mechanism and efficiency of angular momentum transport as well as the level of turbulence in protoplanetary disks (PPDs), which are key to understanding PPD evolution and planet formation. It was shown in our previous work that at 1 AU, the magnetorotational instability (MRI) is completely suppressed when both Ohmic resistivity and ambipolar diffusion (AD) are taken into account, resulting in a laminar flow with accretion driven by magnetocentrifugal wind. In this work, we study the radial dependence of the laminar wind solution using local shearing-box simulations. Scaling relation on the angular momentum transport for the laminar wind is obtained, and we find that the wind-driven accretion rate can be approximated as M_dot~0.91x10^(-8)R_AU^(1.21)(B_z/10mG)^(0.93)M_Sun/yr, where B_z is the strength of the large-scale vertical magnetic field threading the disk. The result is independent of disk surface density. Four criteria are outlined for the existence of the laminar wind solution: 1). Ohmic resistivity dominated midplane region; 2). AD dominated disk upper layer; 3). Presence of (not too weak) net vertical magnetic flux. 4). Sufficiently well ionized gas beyond disk surface. All these criteria are likely to be met in the inner region of the disk from ~0.3 AU to about 5-10 AU for typical PPD accretion rates. Beyond this radius, angular momentum transport is likely to proceed due to a combination of the MRI and disk wind, and eventually dominated by the MRI (in the presence of strong AD) in the outer disk. Our simulation results provide key ingredients for a new paradigm on the accretion processes in PPDs.

Abstract:
The gas dynamics of protoplanetary disks (PPDs) is largely controlled by non-ideal magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion. Among these the role of the Hall effect is the least explored and most poorly understood. We have included all three non-ideal MHD effects in a self-consistent manner to investigate the role of the Hall effect on PPD gas dynamics using local shearing-box simulations. In this first paper, we focus on the inner region of PPDs, where previous studies excluding the Hall effect have revealed that the inner disk up to ~10 AU is largely laminar, with accretion driven by a magnetocentrifugal wind. We confirm this basic picture and show that the Hall effect introduces modest modifications to the wind solutions, depending on the polarity of the large-scale poloidal magnetic field B_0 threading the disk. When B_0.Omega>0, the horizontal magnetic field is strongly amplified toward the disk interior, leading to a stronger disk wind (by ~50% or less in terms of the wind-driven accretion rate). The enhanced horizontal field also leads to much stronger large-scale Maxwell stress (magnetic braking) that contributes to a considerable fraction of the wind-driven accretion rate. When B_0.Omega<0, the horizontal magnetic field is reduced, leading to a weaker disk wind (by ~20%) and negligible magnetic braking. Moreover, we find that when B_0.Omega>0, the laminar region extends farther to ~15 AU before the magneto-rotational instability sets in, while for B_0.Omega<0, the laminar region extends only to ~3-5 AU for a typical PPD accretion rates. Scaling relations for the wind properties, especially the wind-driven accretion rate, are provided for aligned and anti-aligned field geometries. Issues with the symmetry of the wind solutions and grain abundance are also discussed.

Abstract:
We perform 3D stratified shearing-box MHD simulations on the gas dynamics of protoplanetary disks threaded by net vertical magnetic field Bz. All three non-ideal MHD effects, Ohmic resistivity, the Hall effect and ambipolar diffusion are included in a self-consistent manner based on equilibrium chemistry. We focus on regions toward outer disk radii, from 5-60AU, where Ohmic resistivity tends to become negligible, ambipolar diffusion dominates over an extended region across disk height, and the Hall effect largely controls the dynamics near the disk midplane. We find that around R=5AU, the system launches a laminar/weakly turbulent magnetocentrifugal wind when the net vertical field Bz is not too weak, as expected. Moreover, the wind is able to achieve and maintain a configuration with reflection symmetry at disk midplane. The case with anti-aligned field polarity (Omega. Bz<0) is more susceptible to the MRI when Bz drops, leading to an outflow oscillating in radial directions and very inefficient angular momentum transport. At the outer disk around and beyond R=30AU, the system shows vigorous MRI turbulence in the surface layer due to far-UV ionization, which efficiently drives disk accretion. The Hall effect affects the stability of the midplane region to the MRI, leading to strong/weak Maxwell stress for aligned/anti-aligned field polarities. Nevertheless, the midplane region is only very weakly turbulent. Overall, the basic picture is analogous to the conventional layered accretion scenario applied to the outer disk. In addition, we find that the vertical magnetic flux is strongly concentrated into thin, azimuthally extended shells in most of our simulations beyond 15AU. This is a generic phenomenon unrelated to the Hall effect, and leads to enhanced zonal flow. Observational and theoretical implications, as well as future prospects are briefly discussed.

Abstract:
High-resolution positioning for maglev trains is implemented by detecting the tooth-slot structure of the long stator installed along the rail, but there are large joint gaps between long stator sections. When a positioning sensor is below a large joint gap, its positioning signal is invalidated, thus double-modular redundant positioning sensors are introduced into the system. This paper studies switching algorithms for these redundant positioning sensors. At first, adaptive prediction is applied to the sensor signals. The prediction errors are used to trigger sensor switching. In order to enhance the reliability of the switching algorithm, wavelet analysis is introduced to suppress measuring disturbances without weakening the signal characteristics reflecting the stator joint gap based on the correlation between the wavelet coefficients of adjacent scales. The time delay characteristics of the method are analyzed to guide the algorithm simplification. Finally, the effectiveness of the simplified switching algorithm is verified through experiments.