Fragmentation processes in two-phase materials.

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential stress field is tensile. Cracks initiated in this region grow to form meridional planes. If the collision energy exceeds a critical value which depends on the material's internal structure, cracks reach the sample surface resulting in fragmentation. We show that this primary fragmentation mechanism is very robust with respect to the internal structure of the material. For all configurations, a sharp transition from the damage to the fragmentation regime is observed, with smaller critical collision energies for crystalline samples. The mass distribution of the fragments follows a power law for small fragments with an exponent that is characteristic for the branching merging process of unstable cracks. Moreover this exponent depends only on the dimensionally of the system and not on the microstructure.

Morphogenesis of filaments growing in flexible confinements.

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside deformable vesicles or soft tissue-like cell walls, chorions and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements--perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.

Packing of elastic wires in spherical cavities.

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal torsion. We find that the highest packing densities are achieved in low torsion packings for large systems, but in high torsion packings for small systems. An analysis of both situations is given in terms of energetics and comparison is made to analytical models of DNA packing in viral capsids.

Simulation of flow of mixtures through anisotropic porous media using a lattice Boltzmann model.

We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, advection-diffusion, surface tension, and the possibility for global and local viscosity variations to consider various types of hardening fluids. The miscible mixture consists of two fluids, one governed by the hydrodynamic equations and one by advection-diffusion equations. We validate our model on standard problems like Poiseuille flow, the collision of a drop with an impermeable, solid interface and the deformation of the fluid due to surface tension forces. To demonstrate the applicability to complex geometries, we simulate the invasion process of mixtures into wood spruce samples.

Morphological phases of crumpled wire.

We find that in two dimensions wires can crumple into different morphologies and present the associated morphological phase diagram. Our results are based on experiments with different metallic wires and confirmed by numerical simulations using a discrete element model. We show that during crumpling, the number of loops increases according to a power law with different exponents in each morphology. Furthermore, we observe a power law divergence of the structure's bulk stiffness similar to what is observed in forced crumpling of membranes.

Fragmentation processes in impact of spheres.

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.

Scaling behavior of fragment shapes.

We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have shown that the fragments vary from completely isotropic to highly anisotropic elongated shapes, depending on the microscopic cracking mechanism of the shell. Anisotropic fragments proved to have a self-affine character described by a scaling exponent. The distribution of fragment shapes exhibits a power-law decay. The robustness of the scaling laws is illustrated by a stochastic hierarchical model of fragmentation. Our results provide a possible improvement of the representation of fragment shapes in models of space debris.

Breakup of shells under explosion and impact.

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on eggshells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class, different from that of two- and three-dimensional bulk systems.

Fragmentation of shells.

We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.

Effect of the relA gene on derepression of amino acid biosynthetic enzymes in growing Escherichia coli depends on the pathway being derepressed.

Derepression of an enzyme in the arginine biosynthetic pathway, but not of an enzyme in the tryptophan biosynthetic pathway, is inhibited during the stringent response produced by a partial deprivation of valyl transfer ribonucleic acid in a rel+ strain. In contrast, derepression of the tryptophan biosynthetic enzyme, but not of the arginine biosynthetic enzyme, was inhibited during the relaxed response produced in an isogenic relA strain by the partial deprivation of valyl transfer ribonucleic acid.

Effect of the RelA gene on the synthesis of individual proteins in vivo.

We have shown that the relA gene can affect the rates of synthesis of many nonribosomal proteins in E. coli. We used rel+ and relA strains that contain a temperature-sensitive valyl tRNA synthetase. Upon transfer from a permissive temperature (30degreesC) to a semi-resitrictive one (36.5degreesC), these strains continue to grow, although undergoing a partial deprivation of valyl tRNA, In the rel+ strain, the concentration of ppGpp increases immediately, and the accumulation of RNA ceases abruptly but temporarily. In contrast, in the relA strain, the concentration of ppGpp falls, whereas the rate of accumulation of RNA increases. As judged by gel electrophoresis, the rates at which individual polypeptides are synthesized by the strains after their transfer to 36.5degreesC depend to a large extent upon the allelic state of the relA gene. In both strains, the concentration of ppGpp changes soon enough to have altered the synthesis of some of the proteins by affecting the transcription of their genes.

Syntheses of elongation factors Tu and G are under stringent control in Escherichia coli.

We have compared the synthesis of the elongation factors Tu and G at 30 and 36.5 degrees in three strains of Escherichia coli: NF314 (rel+valS+), NF536 (rel+valSts), and NF537 (rel-valSts). At the elevated temperature, the latter two strains continue to grow but suffer a partial deprivation of valyl-tRNA. As a consequence, the syntheses of stable RNA, Tu, and G are decreased in NF536; the syntheses of stable RNA, Tu, and G are increased in NF537. These results indicate that the syntheses of Tu and G are directly or indirectly under the influence of the rel gene.