Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

Novel hydride chemistries are employed to deposit light-emitting Ge_1-y Sn_yalloys with y ≤ 0.1 by Ultra-High Vacuum Chemical Vapor Deposition (UHV-CVD) on Ge-buffered Si wafers. The properties of the resultant materials are systematically compared with similar alloys grown directly on Si wafers. The fundamental difference between the two systems is a fivefold (and higher) decrease in lattice mismatch between film and virtual substrate, allowing direct integration of bulk-like crystals with planar surfaces and relatively low dislocation densities. For y ≤ 0.06, the CVD precursors used were digermane Ge₂H₆ and deuterated stannane SnD₄. For y ≥ 0.06, the Ge precursor was changed to trigermane Ge₃H₈, whose higher reactivity enabled the fabrication of supersaturated samples with the target film parameters. In all cases, the Ge wafers were produced using tetragermane Ge₄H₁₀ as the Ge source. The photoluminescence intensity from Ge_1-y Sn_y /Ge films is expected to increase relative to Ge_1-y Sn_y /Si due to the less defected interface with the virtual substrate. However, while Ge_1-y Sn_y /Si films are largely relaxed, a significant amount of compressive strain may be present in the Ge_1-y Sn_y /Ge case. This compressive strain can reduce the emission intensity by increasing the separation between the direct and indirect edges. In this context, it is shown here that the proposed CVD approach to Ge_1-y Sn_y /Ge makes it possible to approach film thicknesses of about 1  μm, for which the strain is mostly relaxed and the photoluminescence intensity increases by one order of magnitude relative to Ge_1-y Sn_y /Si films. The observed strain relaxation is shown to be consistent with predictions from strain-relaxation models first developed for the Si_1-x Ge_x /Si system. The defect structure and atomic distributions in the films are studied in detail using advanced electron-microscopy techniques, including aberration corrected STEM imaging and EELS mapping of the average diamond–cubic lattice.

We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiple-relation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.

Collective cell migration plays a substantial role in maintaining the cohesion of epithelial cell layers and in wound healing. A number of mathematical models of this process have been developed, all of which reduce to essentially a reaction-diffusion equation with diffusion and proliferation terms that depend on material assumptions about the cell layer. In this paper we extend a one-dimensional mathematical model of cell layer migration of Mi et al. [Biophys. J., 93 (2007), pp. 3745–3752] to incorporate stretch-dependent proliferation, and show that this formulation reduces to a generalized Stefan problem for the density of the layer. We solve numerically the resulting partial differential equation system using an adaptive finite difference method and show that the solutions converge to self-similar or traveling wave solutions. We analyze self-similar solutions for cases with no prolifera- tion, and necessary and sufficient conditions for existence and uniqueness of traveling solutions for a wide range of material assumptions about the cell layer.

The emission properties of GeSn heterostructure pin diodes have been investigated. The devices contain thick (400–600 nm) Ge_1-y Sn_y i-layers spanning a broad compositional range below and above the crossover Sn concentration y_c where the Ge_1-y Sn_y alloy becomes a direct-gap material. These results are made possible by an optimized device architecture containing a single defected interface thereby mitigating the deleterious effects of mismatch-induced defects. The observed emission intensities as a function of composition show the contributions from two separate trends: an increase in direct gap emission as the Sn concentration is increased, as expected from the reduction and eventual reversal of the separation between the direct and indirect edges, and a parallel increase in non-radiative recombination when the mismatch strains between the structure components is partially relaxed by the generation of misfit dislocations. An estimation of recombination times based on the observed electroluminescence intensities is found to be strongly correlated with the reverse-bias dark current measured in the same devices.

The development of non-volatile logic through direct coupling of spontaneous ferroelectric polarization with semiconductor charge carriers is nontrivial, with many issues, including epitaxial ferroelectric growth, demonstration of ferroelectric switching and measurable semiconductor modulation. Here we report a true ferroelectric field effect—carrier density modulation in an underlying Ge(001) substrate by switching of the ferroelectric polarization in epitaxial c-axis-oriented BaTiO₃ grown by molecular beam epitaxy. Using the density functional theory, we demonstrate that switching of BaTiO₃ polarization results in a large electric potential change in Ge. Aberration-corrected electron microscopy confirms BaTiO₃ tetragonality and the absence of any low-permittivity interlayer at the interface with Ge. The non-volatile, switchable nature of the single-domain out-of-plane ferroelectric polarization of BaTiO₃ is confirmed using piezoelectric force microscopy. The effect of the polarization switching on the conductivity of the underlying Ge is measured using microwave impedance microscopy, clearly demonstrating a ferroelectric field effect.