Effect of source strength on dislocation pileups in the presence of stress gradients

The behaviour of a dislocation pileup with a finite-strength source is investigated in the presence of various stress gradients within a continuum model where a free-dislocation region exists around the source. Expressions for dislocation density and stress field within the pileup are derived for the situation where there are first and second spatial gradients in applied stress. For a pileup configuration under an applied stress, yielding occurs when the force acting on the leading dislocations at the pileup tips reaches the obstacle strength, and at the same time, it is required that the source be at the threshold stress for dislocation production. A numerical methodology is presented to solve the underlying equations that represent the yielding conditions. The yield stress calculated for a pileup configuration is found to depend on stress gradients, obstacle spacing and source/obstacle strengths. It increases with increasing the first stress gradient, yet dependent on the second stress gradient. Furthermore, while the dependency of yield stress on the obstacle spacing intensifies with increasing the first stress gradient, it diminishes with an increase of second stress gradient. Therefore, the second stress gradient, as a newly introduced parameter, can provide a new physical insight into the size-dependent plasticity phenomena at small length scales.     

Theoretical investigation on the structure and stability of some neutral noble gas compounds containing Xe-Xe bond

DFT calculations are performed to investigate the structure, stability, and nature of chemical bonding of some neutral noble gas insertion compounds containing a Xe-Xe bond; including HXeXeR, FXeXeR as well as RXeXeR (R = CN, NC, CCH, and BS). Geometry optimization of the considered molecules anticipate the existence of just four stable compounds (HXeXeCN, HXeXeNC, FXeXeCN, and FXeXeCCH); and rest of the molecules dissociate during the structural optimization. The results of NBO and AIM calculations show that a H(F)XeXeR molecule has a covalent H(F)-Xe bond in the H(F)XeXe⁺ fragment, which is bonded to R⁻ mainly through columbic interaction. Thermodynamic study indicates that all of the considered unimolecular dissociation channels for decomposition of H(F)XeXeR molecules to neutral fragments are both exothermic and exorergic; but dissociation to ionic species (H(F)XeXe⁺ and R⁻) is endothermic. Also kinetic study of the most probable dissociation reaction shows that FXeXeR molecules are metastable with respect to the global minimum F-R + 2Xe. Therefore, FXeXeCN molecule is more kinetically protected against the decomposition reaction than the other molecules and its experimental detection is more likely.     

Photoelectron angular distribution of the 3s-subshell of atomic aluminum

Hartree-Fock calculations for the photoelectron angular distribution assymmetry parameters β (^1,3P) for the processes Al 3s²3p(²P) + ω → Al⁺ 3s3p(^1,3P) + e^? are carried out neglecting interchannel interactions. While the β's are found to differ from 2, as predicted for open-shell atom s-subshells by Starace, Rast and Manson, the deviations are found to be rather small in Al due to the absence of Cooper minima in the corresponding photoionization cross sections above threshold.     

A renormalized perturbation theory for problems with non-trivial boundary conditions or backgrounds in two space–time dimensions

We discuss the effects of non-trivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. We present an alternative renormalization procedure in which these non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its n-point functions. To be concrete, we investigate these effects in the λ φ ⁴ model in two dimensions and show that the mass counterterms turn out to be proportional to the Green’s functions which have a non-trivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of non-trivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of non-trivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.     

Chaos-enhanced accelerated particle swarm optimization

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.     

A non-overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two-dimension

We apply a boundary element dual reciprocity method (DRBEM) to the numerical solution of the forward–backward heat equation in a two-dimensional case. The method is employed for the spatial variable via the fundamental solution of the Laplace equation and the Crank–Nicolson finite difference scheme is utilized to treat the time variable. The physical domain is divided into two non-overlapping subdomains resulting in two standard forward and backward parabolic equations. The subproblems are then treated by the underlying method assuming a virtual boundary in the interface and starting with an initial approximate solution on this boundary followed by updating the solution by an iterative procedure. In addition, we show that the time discrete scheme is unconditionally stable and convergent using the energy method. Furthermore, some computational aspects will be suggested to efficiently deal with the formulation of the proposed method. Finally, two forward–backward problems, for which the exact solution is available, will be numerically solved for two different domains to demonstrate the efficiency of the proposed approach.