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.     

Surface Properties of Low Density Polyethylene upon Low-Temperature Plasma Treatment with Various Gases

The surface of a LDPE was modified by Ar, O₂, N₂, CO₂ gaseous plasma. The changes in surface morphology and surface wettability were investigated using AFM and SEM. The surface chemical changes of LDPE were also characterized by FTIR-ATR. The SEM and AFM results demonstrated variable changes in surface roughness for different types of plasma gas used, the changes being more for the Ar and N₂ plasma treatments. Considering the nature of the LDPE film, XRD studies were carried out to determine changes in the percentage crystalinity. The results showed that all low pressure O₂, Ar, N₂, CO₂ gas plasmas improved the wettability of LDPE films. Contact angles decreased significantly depending on the discharge powers and exposure times. Surface morphology was also found to vary with plasma discharge powers, exposure times, and the type of gas being used. Ar and N₂ gas plasmas in general produced more superior results.     

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.     

Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G _C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.     

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.     

Characterizing local rings via homological dimensions and regular sequences

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If the G_C-dimension of M/aM is finite for all ideals a generated by an R-regular sequence of length at most d−t then either the G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.     

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.