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

Mgb2 Nonlinear Properties Investigated under Localized High RF Magnetic Field Excitation

In order to increase the accelerating gradient of Superconducting Radio Frequency (SRF) cavities, Magnesium Diboride (MgB2) opens up hope because of its high transition temperature and potential for low surface resistance in the high RF field regime. However, due to the presence of the small superconducting gap in the {\pi} band, the nonlinear response of MgB2 is potentially quite large compared to a single gap s-wave superconductor (SC) such as Nb. Understanding the mechanisms of nonlinearity coming from the two-band structure of MgB2, as well as extrinsic sources, is an urgent requirement. A localized and strong RF magnetic field, created by a magnetic write head, is integrated into our nonlinear-Meissner-effect scanning microwave microscope [1]. MgB2 films with thickness 50 nm, fabricated by a hybrid physical-chemical vapor deposition technique on dielectric substrates, are measured at a fixed location and show a strongly temperature-dependent third harmonic response. We propose that at least two mechanisms are responsible for this nonlinear response, one of which involves vortex nucleation and penetration into the film. [1] T. M. Tai, X. X. Xi, C. G. Zhuang, D. I. Mircea, S. M. Anlage, "Nonlinear Near-Field Microwave Microscope for RF Defect Localization in Superconductors", IEEE Trans. Appl. Supercond. 21, 2615 (2011).Comment: 6 pages, 6 figure

Liquid Crystal-Solid Interface Structure at the Antiferroelectric-Ferroelectric Phase Transition

Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented

Semiclassical vibrational spectroscopy with Hessian databases

We report on a new approach to ease the computational overhead of ab initio "on-the-fly" semiclassical dynamics simulations for vibrational spectroscopy. The well known bottleneck of such computations lies in the necessity to estimate the Hessian matrix for propagating the semiclassical pre-exponential factor at each step along the dynamics. The procedure proposed here is based on the creation of a dynamical database of Hessians and associated molecular geometries able to speed up calculations while preserving the accuracy of results at a satisfactory level. This new approach can be interfaced to both analytical potential energy surfaces and on-the-fly dynamics, allowing one to study even large systems previously not achievable. We present results obtained for semiclassical vibrational power spectra of methane, glycine, and N-acetyl-L-phenylalaninyl-L-methionine-amide, a molecule of biological interest made of 46 atoms

Rapid crack propagation in loosely fitted PE liner pipe

Published versio

Electronic and magnetic states in doped LaCoO_3

The electronic and magnetic states in doped perovskite cobaltites, (La, Sr)CoO_3, are studied in the numerically exact diagonalization method on Co_2O_{11} clusters. For realistic parameter values, it is shown that a high spin state and an intermediate spin state coexist in one-hole doped clusters due to strong p-d mixing. The magnetic states in the doped cobaltites obtained in the calculation explain various experimental results.Comment: 4 pages, 2 figures, epsfj.st

The phase diagram and bulk thermodynamical quantities in the NJL model at finite temperature and density

We reexamine the recent instanton motivated studies of Alford, Rajagopal and Wilczek, and Berges and Rajagopal in the framework of the standard SU(2) Nambu-Jona-Lasinio model. The chiral phase diagram is calculated in the temperature--density plane, and the pressure is evaluated as the function of the density. Obtaining simple approximate relations describing the $T$-$\mu$ and $T$-$p_F$ phase transition lines we find that the results of the instanton based model and that of the NJL model are identical. The diquark transition line is also given.Comment: 11 pages LaTeX plus 7 PS figures. One figure has been added and there are some changes in the text describing thi

Noseleaf Dynamics during Pulse Emission in Horseshoe Bats

Horseshoe bats emit their biosonar pulses nasally and diffract the outgoing ultrasonic waves by conspicuous structures that surrounded the nostrils. Here, we report quantitative experimental data on the motion of a prominent component of these structures, the anterior leaf, using synchronized laser Doppler vibrometry and acoustic recordings in the greater horseshoe bat (Rhinolophus ferrumequinum). The vibrometry data has demonstrated non-random motion patterns in the anterior leaf. In these patterns, the outer rim of the walls of the anterior leaf twitches forward and inwards to decrease the aperture of the noseleaf and increase the curvature of its surfaces. Noseleaf displacements were correlated with the emitted ultrasonic pulses. After their onset, the inward displacements increased monotonically towards their maximum value which was always reached within the duration of the biosonar pulse, typically towards its end. In other words, the anterior leaf’s surfaces were moving inwards during most of the pulse. Non-random motions were not present in all recorded pulse trains, but could apparently be switched on or off. Such switches happened between sequences of consecutive pulses but were never observed between individual pulses within a sequence. The amplitudes of the emitted biosonar pulse and accompanying noseleaf movement were not correlated in the analyzed data set. The measured velocities of the noseleaf surface were too small to induce Doppler shifts of a magnitude with a likely significance. However, the displacement amplitudes were significant in comparison with the overall size of the anterior leaf and the sound wavelengths. These results indicate the possibility that horseshoe bats use dynamic sensing principles on the emission side of their biosonar system. Given the already available evidence that such mechanisms exist for biosonar reception, it may be hypothesized that time-variant mechanisms play a pervasive role in the biosonar sensing of horseshoe bats

Radseq dataset with 90% missing data fully resolves recent radiation of Petalidium (Acanthaceae) in the ultra-arid deserts of Namibia

Deserts, even those at tropical latitudes, often have strikingly low levels of plant diversity, particularly within genera. One remarkable exception to this pattern is the genus Petalidium (Acanthaceae), in which 37 of 40 named species occupy one of the driest environments on Earth, the Namib Desert of Namibia and neighboring Angola. To contribute to understanding this enigmatic diversity, we generated RADseq data for 47 accessions of Petalidium representing 22 species. We explored the impacts of 18 different combinations of assembly parameters in de novo assembly of the data across nine levels of missing data plus a best practice assembly using a reference Acanthaceae genome for a total of 171 sequence datasets assembled. RADseq data assembled at several thresholds of missing data, including 90% missing data, yielded phylogenetic hypotheses of Petalidium that were confidently and nearly fully resolved, which is notable given that divergence time analyses suggest a crown age for African species of 3.6–1.4 Ma. De novo assembly of our data yielded the most strongly supported and well-resolved topologies; in contrast, reference-based assembly performed poorly, perhaps due in part to moderate phylogenetic divergence between the reference genome, Ruellia speciosa, and the ingroup. Overall, we found that Petalidium, despite the harshness of the environment in which species occur, shows a net diversification rate (0.8–2.1 species per my) on par with those of diverse genera in tropical, Mediterranean, and alpine environments

Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N

We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions at order 1/N, where N is the number of fermion species. We make use of a general formula valid for four-fermion theories, previously applied to the model in 1+1 dimensions. We consider both the discrete and continuous symmetry versions of the model. We show that the pion-like excitations give the dominant contribution at low temperatures. The range of validity for such pion dominance is analyzed. The complete analysis from low to high temperatures also shows that in the critical region the role of composite states is relevant, even for quite large N, and that the free-component behaviour at high T starts at about twice the mean field critical temperature.Comment: 19 pages, RevTeX, 10 figures.p