No abstract

Basquin's law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.

We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

A simple model is presented for the appearance of attraction between two like-charged polyions inside a polyelectrolyte solution. The polyions are modeled as rigid cylinders in a continuum dielectric solvent. The strong electrostatic interaction between the polyions and the counterions results in counterion condensation. If the two polyions are sufficiently close to each other their layers of condensed counterions can become correlated resulting in attraction between the macromolecules. To explore the counterion induced attraction we calculate the correlation functions for the condensed counterions. It is found that the correlations are of very short range. For the parameters specific to the double stranded DNA, the correlations and the attraction appear only when the surface-to-surface separation is less than 7 A.

We have investigated the photoluminescence spectrum of self-assembled InAs quantum dots embedded in a GaAs matrix in magnetic field B up to 23 T and under hydrostatic pressure up to 8 kbar. A strong anisotropy in the diamagnetic shift is found depending on whether B is applied parallel or perpendicular to the growth direction. In the former case, the spatial extent of the carrier wave function in the dot is estimated to be 60 Å. The pressure coefficient for the dot emission line is (9.1±0.2) meV/kbar, about 20% smaller than for the Γ-point band gap in bulk GaAs.

Fractional quantum-Hall-effect features around filling factor v= 2 have been analyzed using the compositefermion approach. Effective masses deduced from the temperature dependence of the Shubnikovde Haas (SdH) oscillations, in agreement with other measurements, show a divergence as the fiiling factor approaches v= z and scale as (density) U . The magnetic-field dependence of the amplitude is explained quantitatively in terms of normal impurity scattering and a strong dephasing term associated with density inhomogeneities of order 0.5%. It is pointed out that assumptions made in the derivation of the standard theory used to analyze SdH oscillations are less likely to be satisfied for composite fermions and that some caution should therefore be used in interpreting effective-mass results obtained in this way. Recently several grou s have used the compositefermion (CF) approach ' to analyze fractional quantum-Hall-effect (FQHE) data. In contrast to the hierarchical model this provides a natural explanation for the strength as well as the position of the FQHE features in terms of Landau-level quantization around even denominator filling factors, in particular around v=-, '. The FQHE energy gaps are then given by the Landau-level spacing fi~, =efiB*/m " where B*=B B / is th-e deviation of the field from the v= -, ' value and m is the composite-fermion effective mass. For electrons the measured values of m are significantly larger than the conventional value (0.067mo)for GaAs and, as predicted, ' scale approximately as B According to gauge arguments the effective mass should diverge logarithmically

We investigate the explosive fragmentation process in two dimensions using molecular-dynamics simulations. We show that the mass distribution of fragments follows a power law, with a scaling exponent that is strongly dependent on the macroscopic characteristics of the system prior to the explosion process. In particular, for thermalized initial configurations at low temperatures, we observe that the exponent is close to -1. We suggest that this result can be interpreted in terms of a multiplicative fracture process.