An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations

DsJ+(2632)D_{sJ}^+(2632): An Excellent Candidate of Tetraquarks

We analyze various possible interpretations of the narrow state $D_{sJ}(2632)$ which lies 100 MeV above threshold. This interesting state decays mainly into $D_s \eta$ instead of $D^0 K^+$. If this relative branching ratio is further confirmed by other experimental groups, we point out that the identification of $D_{sJ}(2632)$ either as a $c\bar s$ state or more generally as a ${\bf {\bar 3}}$ state in the $SU(3)_F$ representation is probably problematic. Instead, such an anomalous decay pattern strongly indicates $D_{sJ}(2632)$ is a four quark state in the $SU(3)_F$ ${\bf 15}$ representation with the quark content ${1\over 2\sqrt{2}} (ds\bar{d}+sd\bar{d}+su\bar{u}+us\bar{u}-2ss\bar{s})\bar{c}$. We discuss its partners in the same multiplet, and the similar four-quark states composed of a bottom quark $B_{sJ}^0(5832)$. Experimental searches of other members especially those exotic ones are strongly called for

Resonant systems for dynamic evaluation of pressure transducers

Tests were conducted with contrived inlet modulated sinusoidal pressure generator to study possible use in calibrating pressure sensors. Results indicate concept is feasible and applicable to transducer evaluation

Melt conditioned direct chill casting (MC-DC) of wrought Al-alloys

Melt Conditioned Direct Chill (MC-DC) casting is a new development for producing high-quality billets and slabs. In the MC-DC process, liquid metal is continuously fed into a MCAST (melt conditioning by advanced shear technology) machine, where the liquid metal is subjected to high shear rate and high degree of turbulence provided by a twin screw mechanism at temperatures either above or below the alloy liquidus, and the conditioned liquid metal is then fed continuously into a Direct Chill (DC) caster to produce billets or slabs. The MC-DC process is applicable to both Aland Mg-alloys. In this paper we present our experimental investigations of the effects of processing parameters on the microstructural and compositional uniformity of 5xxx and 7xxx series Al-alloys. It has been confirmed by our experiments that the MC-DC process can produce billets and slabs with fine and uniform microstructure, uniform chemical compositions and much reduced cast defects, such as porosity and cracks

Helium Recombination Lines as a Probe of Abundance and Temperature Problems

The paper presents a simplified formula to determine an electron temperature, Te(He I), for planetary nebulae (PNe) using the He I 7281/6678 line flux ratio. In our previous studies of Te(He I) (Zhang et al. 2005), we used the He I line emission coefficients given by Benjamin et al. (1999). Here we examine the results of using more recent atomic data presented by Porter et al. (2005). A good agreement is shown, suggesting that the effect of uncertainties of atomic data on the resultant Te(He I) is negligible. We also present an analytical formula to derive electron temperature using the He I discontinuity at 3421 A. Our analysis shows that Te(He I) values are significantly lower than electron temperatures deduced from the Balmer jump of H I recombination spectra, Te(H I), and that inferred from the collisionally excited [O III] nebular-to-auroral forbidden line flux ratio, Te([O III]). In addition, Te(H I) covers a wider range of values than either Te(He I) or Te([O III]). This supports the two-abundance nebular model with hydrogen-deficient material embedded in diffuse gas of a ``normal'' chemical composition (i.e. ~solar).Comment: 5 pages, 3 figures. To appear in the RevMexAA proceedings of "The Ninth Texas-Mexico Conference on Astrophysics

Localization of fermionic fields on braneworlds with bulk tachyon matter

Recently, Pal and Skar in [arXiv:hep-th/0701266] proposed a mechanism to arise the warped braneworld models from bulk tachyon matter, which are endowed with a thin brane and a thick brane. In this framework, we investigate localization of fermionic fields on these branes. As in the 1/2 spin case, the field can be localized on both the thin and thick branes with inclusion of scalar background. In the 3/2 spin extension, the general supergravity action coupled to chiral supermultiplets is considered to produce the localization on both the branes as a result.Comment: 9 pages, no figure