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.     

Rapid extension of a crack

Summary For a body which is initially in a state of uniform anti-plane shear, the wave motion generated by a rapidly extending crack is analyzed in this paper. It is shown that extension with constant speeds of the crack tips is not consistent with the criterion for brittle fracture, but it is consistent with a fracture criterion related to postulated zones of cohesive tractions near the crack tips.

---

Zusammenfassung Anbringen eines Lochs in einem gespannten Körper kann die Entstchung eines rasch sich ausbreitenden Risses veranlassen. In dieser Arbeit wird für einen Körper, der sich ursprünglich in einem Zustand gleichförmiger Schubspannung befand, die durch einen in schneller Ausbreitung begriffenen Riß verursachte Wellenbewegung untersucht. Es wird gezeigt, daß eine Ausbreitung mit konstanten Geschwindigkeiten der Rißenden nicht verträglich ist mit dem Kriterium für Sprödbruch, wohl aber mit einem Bruchkriterium, das mit postulierten Zonen kohäsiver Zugspannungen in der Nähe der Rißenden zusammenhängt.

     

Aziridine-mediated ligation and site-specific modification of unprotected peptides

A synthesis of aziridine-containing peptides via the Cu(II)-promoted coupling of unprotected peptide thioacids and N-H aziridine-2-carbonyl peptides is reported. The unique reactivity of the resulting N-acylated aziridine-2-carbonyl peptides facilitates their subsequent regioselective and stereoselective nucleophilic ring-opening to give unprotected peptides that are specifically modified at the ligation site. The aziridine-mediated peptide ligation concept is exemplified using H(2)O as the nucleophile, producing a Xaa-Thr linkage (where Xaa can be an epimerizable and hindered amino acid). The overall process is compatible with a variety of unprotected amino acid functionality, most notably the N-terminal and Lys side chain amines.     

7,8‐(Dichloromethano)homo[70]fullerene,an Unusual,but Unexceptional,Methanoannulene

The crystal structure of 7,8‐(dichloromethano)homo[70]fullerene shows that addition of the dichlorocarbene (:CCl₂) to C₇₀ gives a surprisingly normal methano‐bridged [9]annulene. The structural changes caused by the addition are highly localized; the C(7)? C(8) distance lengthens by 0.705(2) Å but no other distance changes by more than 0.022(3) Å. Bond angles within the [9]annulene increase by as much as 7.8(1)°, but changes outside the C₉ ring are much smaller. The nearly ellipsoidal molecules form hexagonally close‐packed layers that interact in pairs through short Cl???C, and possibly short Cl???Cl and C???C, interactions.     

Direct measurement of the quantum yield for the creation of mobile excitons from localized states using optically detected electron spin coherence

Optically detected spin locking and adiabatic demagnetization in the rotating frame are used to directly measure the rate constants for trap-to-band promotion and trap-to-trap energy migration in 1,2,4,5-tetrachlorobenzene. Comparison of these rate constants at a given temperature gives the quantum yield for the decay of a promoted localized state into a mobile exciton state. Its dependence on temperature is also determined.     

Diamond a sorting method for vector machines

A method for parallel sorting in vector machines is described. It is shown that it has complexityO(N(logN)²).     

Analysing power for neutron-proton scattering at 14.1 MeV

The analysing power A_γ(θ) for neutron-proton scattering has been measured at 14.1 MeV for c.m. angles between 50° and 157°. A polarized neutron beam was produced by the reaction ${}^3\text{H}\text{(}\text{d}\text{, n}\text{)}{}^4\text{He}$ at 110 keV, using polarized deuterons from an atomic beam polarized ion source. Liquid and plastic scintillators were used for proton targets and the scattered particles were detected in an array of plastic scintillators. Use of the associated alpha technique, multi-parameter recording of events and off-line computer treatment led to very low backgrounds. The results differ significantly from the predictions of the phase-shift analyses of Yale IV, Livermore X and Arndt et al. We find, however, excellent agreement with the predictions of the “Paris potential” of Lacombe et al. Existing n-p analysing power results up to 30 MeV are surveyed and found to be consistent. An attempt was made to look for an isospin splitting of the triplet P-wave phase shifts.