Asymptotic behavior of the potential and existence of a periodic solution for a second order differential equation

We establish the existence of a 2π-periodic solution for a second order semilinear equation in terms of the asymptotic behavior of the potential of the nonlinearity. Our condition includes the case in which the nonlinearity is asymptotically linear with slopes at infinity of the jumping nonlinearity between the positive axes and the first Fucik spectrum curve (see [S. Fucik (1976 Fucik, S. 1976. Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101: 69–87.  [Google Scholar]). Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101, 69–87.]). Our results extend those of [L. Fernandez and F. Zanolin (1988 Fernandez, L. and Zanolin, F. 1988. Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51: 151–163.  [Google Scholar]). Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51, 151–163.].     

Unambiguous evidence for extended s-wave pairing symmetry in hole-doped high-temperature superconductors

We have analysed data from angle-resolved photo-emission spectroscopy, Fourier transform scanning tunneling spectroscopy, and low-temperature thermal conductivity for optimally doped Bi₂Sr₂CaCu₂ O _8+y in order to discriminate between d-wave and extended s-wave pairing symmetry. The combined data are inconsistent with d-wave symmetry, but quantitatively consistent with extended s-wave symmetry with eight line nodes. We also explain all phase-sensitive experiments in a consistent manner.     

A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment.     

Negative stiffness-induced extreme viscoelastic mechanical properties: stability and dynamics

Use of negative stiffness inclusions allows one to exceed the classic bounds upon overall mechanical properties of composite materials. We here analyse discrete viscoelastic ‘spring’ systems with negative stiffness elements to demonstrate the origin of extreme properties, and analyse the stability and dynamics of the systems. Two different models are analysed: one requires geometrical nonlinear analysis with pre-load as a negative stiffness source and the other is a linearized model with a direct application of negative stiffness. Material linearity is assumed for both models. The metastability is controlled by a viscous element. In the stable regime, extreme high mechanical damping tan?δ can be obtained at low frequency. In the metastable regime, singular resonance-like responses occur in tan?δ. The pre-stressed viscoelastic system is stable at the equilibrium point with maximal overall compliance and is metastable when tuned for maximal overall stiffness. A reversal in the relationship between the magnitude of complex modulus and frequency is also observed. The experimental observability of the singularities in tan?δ is discussed in the context of designed composites and polycrystalline solids with metastable grain boundaries.     

Unconventional critical behaviour of fermions hybridized with bosons

A phase transition into the condensed state of fermions hybridized with immobile bosons is examined beyond the ordinary mean-field approximation (MFA) in two and three dimensions. The hybridization interaction does not provide the Cooper pairing of fermions and the Bose condensation in two dimensions. In the three-dimensional boson–fermion model (BFM), an expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg–Landau–Gor’kov equation. This indicates that previous mean-field discussions of the model are flawed in any dimension. In particular, the conventional (MFA) upper critical field is zero in any-dimensional BFM.     

Comparative analysis of uniaxial strain shock tests and Taylor tests for maraging steels

High-strength constructional 38XH3MΦA steel and three kinds of maraging steel were tested to determine the yield stress under dynamic loading. The 38XH3MΦA steel was used as central test material to work out the experimental technique and compare the results obtained in different test methods. Results obtained in the plane shock tests under uniaxial strain condition show roughly the same yield stress values as those obtained in Taylor tests.     

Fullerene-related structure of commercial glassy carbons

Glassy carbon is a technologically important material widely used in products such as electrodes and high-temperature crucibles. However, the properties which make glassy carbon so valuable in these applications are poorly understood, since its detailed atomic structure is not known. A model for the structure of glassy carbon put forward many years ago has gained wide acceptance, but appears to suffer from serious shortcomings. In particular, it fails to account for the chemical inertness of the carbon, and for its high proportion of closed porosity. Here I show, using high-resolution transmission electron microscopy, that glassy carbons obtained from commercial suppliers contain a high proportion of fullerene-related structures. On the basis of these observations, models are put forward for the structures of ‘low-temperature’ and ‘high-temperature’ glassy carbons which incorporate non-six-membered rings.     

Incipient plasticity during nano-scratch in Ni3Al

The subsequent sliding behaviour of the initially elastic, submicron contacts between a diamond tip and bulk polycrystalline Ni₃Al was investigated by nano-scratch tests. Scratches are made under constant normal loads otherwise too low to trigger crystal plasticity in uniaxial nanoindentation experiments. Three types of behaviour are observed: (i) the entire scratch is purely elastic with a sliding coefficient of friction (μ) of about 0.086; (ii) a sudden strain burst in the normal direction, commonly known as pop-in, occurs at the onset of sliding and the subsequent sliding is plastic with μ typically a few times larger than 0.086; and (iii) an intermediate case in which the scratch is initially elastic followed by a pop-in beyond which the sliding becomes plastic. The intermediate case occurs rather randomly. The μ for elastic sliding is found to be load- or size-independent, but that for plastic sliding exhibits a strong size effect, i.e. it is small at small loads, but increases towards a steady value at larger loads.