Modified extragradient methods for solving variational inequalities

AbstractIn this paper, we propose two methods for solving variational inequalities. In the first method, we modified the extragradient method by using a new step size while the second method can be viewed as an extension of the first one by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. Under certain conditions, the global convergence of two methods is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed methods

Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.Comment: 6 pages, two figures .Presented at the International Symposium on Quantum Fluids and Solids QFS2006 (Kyoto, Japan

A new displacement-based approach to calculate stress intensity factors with the boundary element method

The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has be-come very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes

Theory of nonlinear Landau-Zener tunneling

A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear parameter $C$ is above a critical value equal to the gap $V$ of avoided crossing of the two levels. In this paper, we present analytical results that give quantitative account of the breakdown of adiabaticity by mapping this quantum nonlinear model into a classical Josephson Hamiltonian. In the critical region, we find a power-law scaling of the nonadiabatic transition probability as a function of $C/V-1$ and $\alpha$, the crossing rate of the energy levels. In the subcritical regime, the transition probability still follows an exponential law but with the exponent changed by the nonlinear effect. For $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.Comment: 9 figure

Single photon emitters based on Ni/Si related defects in single crystalline diamond

We present investigations on single Ni/Si related color centers produced via ion implantation into single crystalline type IIa CVD diamond. Testing different ion dose combinations we show that there is an upper limit for both the Ni and the Si dose 10^12/cm^2 and 10^10/cm^2 resp.) due to creation of excess fluorescent background. We demonstrate creation of Ni/Si related centers showing emission in the spectral range between 767nm and 775nm and narrow line-widths of 2nm FWHM at room temperature. Measurements of the intensity auto-correlation functions prove single-photon emission. The investigated color centers can be coarsely divided into two groups: Drawing from photon statistics and the degree of polarization in excitation and emission we find that some color centers behave as two-level, single-dipole systems whereas other centers exhibit three levels and contributions from two orthogonal dipoles. In addition, some color centers feature stable and bright emission with saturation count rates up to 78kcounts/s whereas others show fluctuating count rates and three-level blinking.Comment: 7 pages, submitted to Applied Physics B, revised versio

Facile Synthesis of ZnO Nanorods by Microwave Irradiation of Zinc–Hydrazine Hydrate Complex

ZnO nanorods have been successfully synthesized by a simple microwave-assisted solution phase approach. Hydrazine hydrate has been used as a mineralizer instead of sodium hydroxide. XRD and FESEM have been used to characterize the product. The FESEM images show that the diameter of the nanorods fall in the range of about 25–75 nm and length in the range of 500–1,500 nm with an aspect ratio of about 20–50. UV–VIS and photoluminescence spectra of the nanorods in solution have been taken to study their optical properties. A mechanism for microwave synthesis of the ZnO nanorods using hydrazine hydrate precursor has also been proposed

Bomb-¹⁴C analysis of ecosystem respiration reveals that peatland vegetation facilitates release of old carbon

The largest terrestrial-to-atmosphere carbon flux is respired CO<sub>2</sub>. However, the partitioning of soil and plant sources, understanding of contributory mechanisms, and their response to climate change are uncertain. A plant removal experiment was established within a peatland located in the UK uplands to quantify respiration derived from recently fixed plant carbon and that derived from decomposition of soil organic matter, using natural abundance <sup>13</sup>C and bomb-<sup>14</sup>C as tracers. Soil and plant respiration sources were found respectively to contribute ~ 36% and between 41-54% of the total ecosystem CO<sub>2</sub> flux. Respired CO<sub>2</sub> produced in the clipped (‘soil’) plots had a mean age of ~ 15 years since fixation from the atmosphere, whereas the <sup>14</sup>C content of ecosystem CO<sub>2</sub> was statistically indistinguishable from the contemporary atmosphere. Results of carbon mass balance modelling showed that, in addition to respiration from bulk soil and plant respired CO<sub>2</sub>, a third, much older source of CO<sub>2</sub> existed. This source, which we suggest is CO<sub>2</sub> derived from the catotelm constituted between ~ 10 and 23% of total ecosystem respiration and had a mean radiocarbon age of between several hundred to ~ 2000 years before present (BP). These findings show that plant-mediated transport of CO<sub>2</sub> produced in the catotelm may form a considerable component of peatland ecosystem respiration. The implication of this discovery is that current assumptions in terrestrial carbon models need to be re-evaluated to consider the climate sensitivity of this third source of peatland CO<sub>2</sub>

Charge Transport Through Open, Driven Two-Level Systems with Dissipation

We derive a Floquet-like formalism to calculate the stationary average current through an AC driven double quantum dot in presence of dissipation. The method allows us to take into account arbitrary coupling strengths both of a time-dependent field and a bosonic environment. We numerical evaluate a truncation scheme and compare with analytical, perturbative results such as the Tien-Gordon formula.Comment: 14 pages, 6 figures. To appear in Phys. Rev.

Wear and damage transitions of wheel and rail materials under various contact conditions

This study discusses a Tγ/A method of plotting wear data from a twin-disc machine for identifying the wear and damage transitions of wheel and rail materials. As found in previous work, three wear regimes (mild wear, severe wear and catastrophic wear) of U71Mn rail material were identified in dry rolling-sliding contact tests. It was determined that the damage mechanism transforms in the different wear regimes. Here earlier studies were extended to establish wear behavior for the presence of a number of third body materials (oil, water, friction enhancers) and a rail cladding process designed to make wheels and rails more durable. This has provided much needed data for Multi-Body Dynamics (MBD) simulations, and will allow better predictions of profile evolution of wheel and rail over a wider range of conditions

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.