Mathematical and Numerical Studies on Meshless Methods for Exterior Unbounded Domain Problems

The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation is ill-conditioned. A modified MFS (MMFS) with the proper basis functions is proposed by the introduction of the modified Trefftz method (MTM). The concrete expressions of the corresponding condition numbers and the solvability by these methods are mathematically proven. Thereby, the optimal parameter minimizing the condition number is also mathematically given. Numerical experiments show that the condition numbers of the matrices corresponding to the MTM and the MMFS are reduced and that the numerical solution by the MMFS is more accurate than the one by the conventional method.Comment: 25 pages, 11 figure

Recent developments of SPH in modeling explosion and impact problems

Explosion and impact problems are generally characterized by the presence of shock waves, intense localized materials response and intensive loadings. Most of the wave propagation hydro-codes for such problems use traditional grid based methods such as finite difference methods (FDM) and finite element methods (FEM). Though many successful achievements have been made using these methods, some numerical difficulties still exist. These numerical difficulties generally arise from large deformations, large inhomogeneities, and moving interfaces, free or movable boundaries. Smoothed particle hydrodynamics (SPH) is a Lagrangian, meshfree particle method, and has been widely applied to different areas in engineering and science. SPH method has been intensively used for simulating high strain hydrodynamics with material strength, due to its special features of meshfree, Lagrangian and particle nature. In this paper, some recent developments of the SPH in modelling explosion and impact problems will be introduced. A modified scheme for approximating kernel gradient (kernel gradient correction, or KGC) has been used in the SPH simulation to achieve better accuracy and stability. The modified SPH method is used to simulate a number of problems including 1D TNT detonation, linear shaped charge and explosively driven welding. The effectiveness of the modified SPH method has been demonstrated by comparative studies of the SPH results with data from other resources.Peer ReviewedPostprint (published version

A Study of Radioxenon Production from Proton Bombardment of Metallic Cesium

This work was supported by National Science Foundation Grant PHY 76-84033 and Indiana Universit

Oxygen impurities in NiAl: Relaxation effects

We have used a full-potential linear muffin-tin orbital method to calculate the effects of oxygen impurities on the electronic structure of NiAl. Using the supercell method with a 16-atom supercell we have investigated the cases where an oxygen atom is substitutionally placed at either a nickel or an aluminum site. Full relaxation of the atoms within the supercell was allowed. We found that oxygen prefers to occupy a nickel site over an aluminum site with a site selection energy of 138 mRy (21,370 K). An oxygen atom placed at an aluminum site is found to cause a substantial relaxation of its nickel neighbors away from it. In contrast, this steric repulsion is hardly present when the oxygen atom occupies the nickel site and is surrounded by aluminum neighbors. We comment on the possible relation of this effect to the pesting degradation phenomenon (essentially spontaneous disintegration in air) in nickel aluminides.Comment: To appear in Phys. Rev. B (Aug. 15, 2001

The X10 Flare on 2003 October 29: Triggered by Magnetic Reconnection between Counter-Helical Fluxes?

Vector magnetograms taken at Huairou Solar Observing Station (HSOS) and Mees Solar Observatory (MSO) reveal that the super active region (AR) NOAA 10486 was a complex region containing current helicity flux of opposite signs. The main positive sunspots were dominated by negative helicity fields, while positive helicity patches persisted both inside and around the main positive sunspots. Based on a comparison of two days of deduced current helicity density, pronounced changes were noticed which were associated with the occurrence of an X10 flare that peaked at 20:49 UT, 2003 October 29. The average current helicity density (negative) of the main sunspots decreased significantly by about 50. Accordingly, the helicity densities of counter-helical patches (positive) were also found to decay by the same proportion or more. In addition, two hard X-ray (HXR) `footpoints' were observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI} during the flare in the 50-100 keV energy range. The cores of these two HXR footpoints were adjacent to the positions of two patches with positive current helicity which disappeared after the flare. This strongly suggested that the X10 flare on 2003 Oct. 29 resulted from reconnection between magnetic flux tubes having opposite current helicity. Finally, the global decrease of current helicity in AR 10486 by ~50% can be understood as the helicity launched away by the halo coronal mass ejection (CME) associated with the X10 flare.Comment: Solar Physics, 2007, in pres

A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Nonlinear Volatility of River Flux Fluctuations

We study the spectral properties of the magnitudes of river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) strongly power-law correlations for time scales less than one year. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than one year. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.Comment: 5 revtex pages, 6 page

Analysis of Bi Distribution in Epitaxial GaAsBi by aberration-corrected HAADF-STEM

The Bi content in GaAs/GaAs1 − xBix/GaAs heterostructures grown by molecular beam epitaxy at a substrate temperature close to 340 °C is investigated by aberration-corrected high-angle annular dark-field techniques. The analysis at low magnification of high-angle annular dark-field scanning transmission electron microscopy images, corroborated by EDX analysis, revealed planar defect-free layers and a non-homogeneous Bi distribution at the interfaces and within the GaAsBi layer. At high magnification, the qHAADF analysis confirmed the inhomogeneous distribution and Bi segregation at the GaAsBi/GaAs interface at low Bi flux and distorted dumbbell shape in areas with higher Bi content. At higher Bi flux, the size of the Bi gathering increases leading to roughly equiaxial Bi-rich particles faceted along zinc blende {111} and uniformly dispersed around the matrix and interfaces. FFT analysis checks the coexistence of two phases in some clusters: a rhombohedral pure Bi (rh-Bi) one surrounded by a zinc blende GaAs1 − xBix matrix. Clusters may be affecting to the local lattice relaxation and leading to a partially relaxed GaAsBi/GaAs system, in good agreement with XRD analysis

Synchrotron emission from secondary leptons in microquasar jets

We present a model to estimate the synchrotron radio emission generated in microquasar (MQ) jets due to secondary pairs created via decay of charged pions produced in proton-proton collisions between stellar wind ions and jet relativistic protons. Signatures of electrons/positrons are obtained from consistent particle energy distributions that take into account energy losses due to synchrotron and inverse Compton (IC) processes, as well as adiabatic expansion. The space parameter for the model is explored and the corresponding spectral energy distributions (SEDs) are presented. We conclude that secondary leptonic emission represents a significant though hardly dominant contribution to the total radio emission in MQs, with observational consequences that can be used to test some still unknown processes occurring in these objects as well as the nature of the matter outflowing in their jets