Porous Functional Graded Bioceramics with Integrated Interface Textures

Porous functional graded ceramics (porous FGCs) offer immense potential to overcome the low mechanical strengths of homogeneously porous bioceramics used as bone grafts. The tailored manipulation of the graded pore structure including the interfaces in these materials is of particular interest to locally control the microstructural and mechanical properties, as well as the biological response of the potential implant. In this work, porous FGCs with integrated interface textures were fabricated by a novel two-step transfer micro-molding technique using alumina and hydroxyapatite feedstocks with varied amounts of spherical pore formers (0–40 Vol%) to generate well-defined porosities. Defect-free interfaces could be realized for various porosity pairings, leading to porous FGCs with continuous and discontinuous transition of porosity. The microstructure of three different periodic interface patterns (planar, 2D-linear waves and 3D-Gaussian hills) was investigated by SEM and µCT and showed a shape accurate replication of the CAD-designed model in the ceramic sample. The Young’s modulus and flexural strength of bi-layered bending bars with 0 and 30 Vol% of pore formers were determined and compared to homogeneous porous alumina and hydroxyapaite containing 0–40 Vol% of pore formers. A significant reduction of the Young’s modulus was observed for the porous FGCs, attributed to damping effects at the interface. Flexural 4-point-testing revealed that the failure did not occur at the interface, but rather in the porous 30 Vol% layer, proving that the interface does not represent a source of weakness in the microstructure.

When to wake up? The optimal waking-up strategies for starvation-induced persistence

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.

Discontinuous transition to loop formation in optimal supply networks

The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding redundant edges to supply networks is costly, yet beneficial for resilience. Loops typically form when costs for new edges are small or inputs uncertain. Here, we shed further light on the transition to loop formation. We demonstrate that loops emerge discontinuously when decreasing the costs for new edges for both an edge-damage model and a fluctuating sink model. Mathematically, new loops are shown to form through a saddle-node bifurcation. Our analysis allows to heuristically predict the location and cost where the first loop emerges. Finally, we unveil an intimate relationship among betweenness measures and optimal tree networks. Our results can be used to understand the evolution of loop formation in real-world biological networks.

q-Neighbor Ising model on random networks

A modified kinetic Ising model with Metropolis dynamics, so-called [Formula: see text]-neighbor Ising model, is investigated on random graphs. In this model, each spin interacts only with [Formula: see text] spins randomly chosen from its neighborhood. Investigations are performed by means of Monte Carlo (MC) simulations and the analytic pair approximation (PA). The range of parameters such as the size of the [Formula: see text]-neighborhood and the mean degree of nodes of the random graph is determined for which the model exhibits continuous or discontinuous ferromagnetic (FM) phase transition with decreasing temperature. It is also shown that, in the case of discontinuous transition for large enough and fixed mean degree of nodes, the width of the hysteresis loop oscillates with the parameter [Formula: see text], expanding for even and shrinking for odd values of [Formula: see text]. Predictions of the PA show satisfactory quantitative agreement with results of MC simulations.