On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Surface and vortex structures in noncentrosymmetric superconductors under applied magnetic fields

We investigate how the macroscopic spatial structure of broken inversion symmetry manifests in noncentrosymmetric superconductors, by the microscopic broken inversion symmetry of the crystal structure. Based on the time-dependent Ginzburg-Landau theory including the Pauli paramagnetic effect and the Rashba interaction, we demonstrate that the centrosymmetric structures of the internal field and the screening current are broken macroscopically. The flow structure of paramagnetic supercurrent spontaneously induce the flux flow without applying external currents.Comment: 5 pages, 8 figures. accepted in Phys. Rev.

Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page

Influence of hydrogen on the structural stability of annealed ultrathin Si/Ge amorphous layers

Semiconductor structures based on Si and Ge are generally submitted to hydrogenation because H passivates the dangling bonds of Si and Ge. By this way the devices prepared from those semiconductors, e.g., solar cells, have much better electrical properties. However, H stability is still a critical issue. In fact, there is wide evidence that H is very unstable against illumination as well as heat treatment. It has been seen that H out effuses from the samples under such treatments. As this causes unsaturation of the dangling bonds the electrical properties worsen significantly. In this work we will show that in the case of ultrathin Si/Ge amorphous layers the H thermal instability also affects the structural stability even up to the micrometric scale depending on the H content. Such type of structure can also be used to prepare SiGe alloys by mixing the layers with heat treatments. The samples were amorphous multilayers (MLs) of alternating ultrathin (3 nm) layers of Si and Ge deposited by sputtering on (100) oriented Si substrate. The total thickness of the MLs was 300 nm. The samples were hydrogenated by introducing H in the sputter chamber with flow rates varying from 0.8 to 6 ml/min. The MLs underwent different heat treatments, from the one at 350 ?C for 1 h up to the one at 250 ?C for 0.5 h + 450 ?C for 5 h. The samples were analysed by AFM, TEM, energy filtering TEM and Small-Angle X-Ray Diffraction (SAXRD). AFM showed that upon annealing the structure of the samples degrades with formation of surface bumps whose size increases by increasing the annealing temperature and/or time, for the same H content, or by increasing the H content for the same annealing conditions. For high H content and/or annealing conditions AFM showed that the bumps have blown up giving rise to craters. This suggests that H was released from its dangling bonds to Si and Ge and formed H bubbles in the MLs because of the energy supplied by the annealing. Additional energy for the break of the Si-H and Ge-H bonds could be the one supplied by the recombination of thermally generated carriers associated with the band gap fluctuations caused by the not uniform distribution of H in the MLs. The first sites of H accumulation are very likely nanocavities certainly present in the amorphous MLs. By TEM it has been seen that layer intermixing occurred which could be the first step of H bubbles formation. SAXRD measurements as well as TEM energy filtering maps for Si and Ge showed that Si and Ge interdiffusion took place in an asymmetric way as Si was seen to diffuse to the Ge layers whereas Ge did not diffuse to the Si layers. This might be due to the higher density of free dangling bonds in the Ge layers created by annealing because the binding energy of the Ge-H bond is smaller than the one of the Si-H bond

Modelling of broadband light sources based on InAs / INxGA1-xAS metamorphic quantum dots

We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAs quantum dots (QDs) embedded into a metamorphic 4-step-graded InxGa1- xAs buffer with x = 0.10, 0.20, 0.30, 0.40. We developed a model to calculate metamorphic QD energy levels based on realistic QD parameters and on strain-dependent material properties: results of simulations were validated against experimental values. By simulating the broadband metamorphic structure, we demonstrated that its light emission can cover the whole 1.0 - 1.7 μm range with a bandwidth of 550 nm at 10K. The emission spectrum was then assessed under realistic electrical injection conditions, at room temperature, through device-level simulations based on a coupled drift-diffusion and QD dynamics model. As metamorphic QD devices have been already fabricated with satisfying performances we believe that this proposal is a viable option to realize broader band light-emitting devices such as superluminescent diodes

Broadband light sources based on InAs/InGaAs metamorphic quantum dots

We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAsquantum dots(QDs) embedded into a metamorphic step-graded InxGa1−xAs buffer. We developed a model to calculate the metamorphic QD energy levels based on the realistic QD parameters and on the strain-dependent material properties; we validated the results of simulations by comparison with the experimental values. On this basis, we designed a p-i-n heterostructure with a graded index profile toward the realization of an electrically pumped guided wave device. This has been done by adding layers where QDs are embedded in InxAlyGa1−x−yAs layers, to obtain a symmetric structure from a band profile point of view. To assess the room temperature electro-luminescenceemission spectrum under realistic electrical injection conditions, we performed device-level simulations based on a coupled drift-diffusion and QD rate equation model. On the basis of the device simulation results, we conclude that the present proposal is a viable option to realize broadband light-emitting devices

Nuclear Magnetic Relaxation Rate in a Noncentrosymmetric Superconductor

For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We demonstrate that such a model on a qualitative level accounts for experimentally observed features of the temperature dependence of the nuclear spin-lattice relaxation rate 1/T1, namely a peak just below Tc and a line-node gap behavior at low temperatures.Comment: 4 page

The determinants of transverse tubular volume in resting skeletal muscle.

The transverse tubular (t)-system of skeletal muscle couples sarcolemmal electrical excitation with contraction deep within the fibre. Exercise, pathology and the composition of the extracellular fluid (ECF) can alter t-system volume (t-volume). T-volume changes are thought to contribute to fatigue, rhabdomyolysis and disruption of excitation-contraction coupling. However, mechanisms that underlie t-volume changes are poorly understood. A multicompartment, history-independent computer model of rat skeletal muscle was developed to define the minimum conditions for t-volume stability. It was found that the t-system tends to swell due to net ionic fluxes from the ECF across the access resistance. However, a stable t-volume is possible when this is offset by a net efflux from the t-system to the cell and thence to the ECF, forming a net ion cycle ECF→t-system→sarcoplasm→ECF that ultimately depends on Na(+)/K(+)-ATPase activity. Membrane properties that maximize this circuit flux decrease t-volume, including PNa(t) > PNa(s), PK(t) < PK(s) and N(t) < N(s) [P, permeability; N, Na(+)/K(+)-ATPase density; (t), t-system membrane; (s), sarcolemma]. Hydrostatic pressures, fixed charges and/or osmoles in the t-system can influence the magnitude of t-volume changes that result from alterations in this circuit flux. Using a parameter set derived from literature values where possible, this novel theory of t-volume was tested against data from previous experiments where t-volume was measured during manipulations of ECF composition. Predicted t-volume changes correlated satisfactorily. The present work provides a robust, unifying theoretical framework for understanding the determinants of t-volume.JAF was supported by a David Phillips Fellowship (BB/FO23863/1) awarded by the Biotechnology and Biological Sciences Research Council (UK). JS was supported by the Agency for Science, Technology and Research (Singapore) and a Caius Medical Association summer studentship from Gonville and Caius College, University of Cambridge.This is the final version. It was first published by Wiley at http://onlinelibrary.wiley.com/doi/10.1113/jphysiol.2014.281170/abstract