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

Trapped interacting two-component bosons

In this paper we solve one dimensional trapped SU(2) bosons with repulsive $\delta$-function interaction by means of Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin "ferromagnetic" state which differs from spin-1/2 fermions system. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The thermodynamics equilibrium of the system at finite temperature is studied by thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat etc. are obtained for the case of strong coupling limit.Comment: 15 pages, 9 figure

Fermionic concurrence in the extended Hubbard dimer

In this paper, we introduce and study the fermionic concurrence in a two-site extended Hubbard model. Its behaviors both at the ground state and finite temperatures as function of Coulomb interaction $U$ (on-site) and $V$ (nearest-neighbor) are obtained analytically and numerically. We also investigate the change of the concurrence under a nonuniform field, including local potential and magnetic field, and find that the concurrence can be modulated by these fields.Comment: 5 pages, 7 figure

A Cosmological Model with Dark Spinor Source

In this paper, we discuss the system of Friedman-Robertson-Walker metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the Universe to become singular. The solution is oscillating in time and closed in space, which approximately takes the following form g_{\mu\nu}=\bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r ,-\sin^2r \sin^2\theta), with $\bar R= (1\sim 2)\times 10^{12}$ light year, and $\delta=0.96\sim 0.99$. The present time is about $t\sim 18^\circ$.Comment: 13 pages, no figure, to appear in IJMP

Redundant regulation of meristem identity and plant architecture by FRUITFULL, APETALA1 and CAULIFLOWER

The transition from vegetative to reproductive phases during Arabidopsis development is the result of a complex interaction of environmental and endogenous factors. One of the key regulators of this transition is LEAFY (LFY), whose threshold levels of activity are proposed to mediate the initiation of flowers. The closely related APETALA1 (AP1) and CAULIFLOWER (CAL) meristem identity genes are also important for flower initiation, in part because of their roles in upregulating LFY expression. We have found that mutations in the FRUITFULL (FUL) MADS-box gene, when combined with mutations in AP1 and GAL, lead to a dramatic non-flowering phenotype in which plants continuously elaborate leafy shoots in place of flowers. We demonstrate that this phenotype is caused both by the lack of LFY upregulation and by the ectopic expression of the TERMINAL FLOWER1 (TFL1) gene. Our results suggest that the FUL, AP1 and CAL genes act redundantly to control inflorescence architecture by affecting the domains of LFY and TFL1 expression as well as the relative levels of their activities

The FRUITFULL MADS-box gene mediates cell differentiation during Arabidopsis fruit development

Fruit morphogenesis is a process unique to flowering plants, and yet little is known about its developmental control, Following fertilization, fruits typically undergo a dramatic enlargement that is accompanied by differentiation of numerous distinct cell types. We have identified a mutation in Arabidopsis called fruitfull (ful-1), which abolishes elongation of the silique after fertilization. The ful-1 mutation is caused by the insertion of a DsE transposable enhancer trap element into the 5' untranslated leader of the AGL8 MADS-box gene. beta-glucuronidase (GUS) reporter gene expression in the enhancer trap line is observed specifically in all cell layers of the valve tissue, but not in the replum, the septum or the seeds, and faithfully mimics RNA in situ hybridization data reported previously, The lack of coordinated growth of the fruit tissues leads to crowded seeds, a failure of dehiscence and, frequently, the premature rupture of the carpel valves, The primary defect of ful-1 fruits is within the valves, whose cells fail to elongate and differentiate. Stomata, which are frequent along the epidermis of wild-type valves, are completely eliminated in the ful mutant valves. In addition to the effect on fruit development, ful cauline leaves are broader than those of wild type and show a reduction in the number of internal cell layers. These data suggest that AGL8/FUL regulates the transcription of genes required for cellular differentiation during fruit and leaf development

Ground-state fidelity of Luttinger liquids: A wave functional approach

We use a wave functional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground-state wave functionals are discussed using both the Schrodinger (functional differential equation) formulation and a path integral formulation. The fidelity between Luttinger liquids with Luttinger parameters K and K' is found to decay exponentially with system size, and to obey the symmetry F(K,K')=F(1/K,1/K') as a consequence of a duality in the bosonization description of Luttinger liquids.Comment: 13 pages, IOP single-column format. Sec. 3 expanded with discussion of short-distance cut-off. Some typos corrected. Ref. 44 in v2 is now footnote 2 (moved by copy editor). Published versio