Prevalence and Significance of Approximate Symmetry in Organic Pc Structures

A survey has been made of the well determined (R≤0.050) organic crystal structures that have only a single glide plane (e. g., are in space group Pc) and that have more than one crystallographically independent formula unit (Z′>1); the goal was to discover what fraction have additional approximate symmetry. Of the 377 unique structures examined 8 % should almost certainly been refined in a higher-symmetry unit cell; 86 % of the remaining 347 have approximate symmetry that is periodic in at least one dimension. While these percentages are similar to those found for P1 structures (C. P. Brock, Acta Crystallogr., Sect. B 2022 , 78, 576–588), the types of approximate symmetry differ because 89 % of the P1, Z′>1 structures were composed of enantiopure material. The 347 reliable Pc structures include 118 that are slightly distorted or mimicked Cc and P2₁/c structures, 15 of which were reported as having been determined at room temperature. The distortions in another 72 are so large that the approximate symmetry must be seen as periodic in two dimensions only. These results suggest that symmetry lowering may accompany transformation of a crystal nucleus to a macroscopic crystal.     

Dynamic frictional indentation of an elastic half-plane by a rigid punch

Dynamic rigid indentation of a linearly elastic half-plane in the presence of Coulomb friction is studied in this paper. A rigid punch, which is either wedge- or parabolic-shaped, is rapidly driven into the deformable body so that stress waves are generated. The contact region is assumed to extend at a constant sub-Rayleigh speed (this situation can be achieved by conveniently specifying the kinetic and geometric characteristics of indentor), whereas, due to symmetry, friction acts in opposing directions on opposite sides of the indentor. As the present exact analysis shows, this sign reversal of the tangential traction along the half-plane surface creates an extra stress-singularity at the changeover point of the boundary conditions (due to symmetry, this point here coincides with the point where the indentor apex makes contact with the half-plane surface). The study exploits the problem's self-similarity by utilizing homogeneous-function techniques previously used by L.M. Brock, along with the Riemann-Hilbert problem analysis. Representative numerical results are given for the wedge indentation case.     

Bounds on an anomalous dijet resonance in W+jets production in pp collisions at √s = 1.96 TeV

We present a study of the dijet invariant mass spectrum in events with two jets produced in association with a W boson in data corresponding to an integrated luminosity of 4.3 fb(-1) collected with the D0 detector at √s = 1.96 TeV. We find no evidence for anomalous resonant dijet production and derive upper limits on the production cross section of an anomalous dijet resonance recently reported by the CDF Collaboration, investigating the range of dijet invariant mass from 110 to 170 GeV/c(2). The probability of the D0 data being consistent with the presence of a dijet resonance with 4 pb production cross section at 145 GeV/c(2) is 8×10(-6).     

Search for Resonant WW and WZ Production in pp collisions at √s=1.96 TeV

We search for resonant WW or WZ production by using up to 5.4 fb(-1) of integrated luminosity collected by the D0 experiment in run II of the Fermilab Tevatron Collider. The data are consistent with the standard model background expectation, and we set limits on a resonance mass by using the sequential standard model W' boson and the Randall-Sundrum model graviton G as benchmarks. We exclude a sequential standard model W' boson in the mass range 180-690 GeV and a Randall-Sundrum graviton in the range 300-754 GeV at 95% C.L.     

Multilayer thin-film inspection through measurements of reflection coefficients

A vibration-insensitive interferometer is described to measure the thickness, refraction index and surface profile of thin-film stack at normal incidence. By satisfying the continuous boundary conditions of electric and magnetic fields at interfaces in a multilayer film stack, the reflection coefficient phase of the thin-film stack can be distinguished from the phase of spatial path difference, thus thickness and refraction index can be extracted. The experiment results showed that the measurement precision is significantly increased after the phase analysis was added into the reflectance analysis.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch

Static rigid 2-D indentation of a linearly elastic half-plane in the presence of Coulomb friction which reverses its sign along the contact length is studied. The solution approach lies within the context of the mathematical theory of elastic contact mechanics. A rigid punch, having an unsymmetrical profile with respect to its apex and no concave regions, both slides over and indents slowly the surface of the deformable body. Both a normal and a tangential force may, therefore, be exerted on the punch. In such a situation, depending upon the punch profile and the relative magnitudes of the two external forces, a point in the contact zone may exist at which the surface friction changes direction. Moreover, this point of sign reversal may not coincide, in general, with the indentor's apex. This position and the positions of the contact zone edges can be determined only by first constructing a solution form containing the three problem's unspecified lengths, and then solving numerically a system of non-linear equations containing integrals not available in closed form.The mathematical procedure used to construct the solution deals with the Navier-Cauchy partial differential equations (plane-strain elastostatic field equations) supplied with boundary conditions of a mixed type. We succeed in formulating a second-kind Cauchy singular integral equation and solving it exactly by analytic-function theory methods.Representative numerical results are presented for two indentor profiles of practical interest—the parabola and the wedge.     

A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative

We develop a new method to prove symmetry results for overdetermined boundary value problems. This method is based on the use of continuous Steiner symmetrization together with derivative with respect to the domain. It allows to consider nonlinear equations in divergence form with dependence inr=|x| in the nonlinearity. By using the notion of “local symmetry” introduced by the first author, we prove that the domain is necessarily a ball. We also give an example where the solution of the overdetermined problem is not radially symmetric.     

Nanoindentation and Microindentation of CuAlNi Shape Memory Alloy

Nanoindentation and microindentation studies were conducted within individual grains of a CuAlNi shape memory alloy. Linear surface features were observed near the indentations after unloading, many of which were responsive to heating. Crystallographic orientation information was obtained from electron backscattering diffraction in order to compare the orientation of observed surface features to predicted austenite–martensite interfaces, slip planes, and possible fracture planes in this alloy. Most of the features observed can be attributed to austenite–martensite interfaces, which remain in the material after unloading due to the constraints of the plastic deformation created by indentation. Due to the temperature dependence of the transformation stress in shape memory alloys, these stress-induced martensites are observed to diminish with heating and to reappear with cooling. Plastic deformation is observed in the form of pile-up near the indentation.