Encapsulated formulation of the Selective Frequency Damping method

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a "black box". The method is first applied to a scalar problem in order to analyse its stability and highlight the roles of the control coefficient $\chi$ and the filter width $\Delta$ in the convergence (or not) towards the steady-state. Then the steady-state of the incompressible flow past a two-dimensional cylinder at $Re=100$, obtained with a code which implements the spectral/hp element method, is presented

Predicted elastic constants and critical layer thicknesses for cubic phase AlN, GaN, and InN on β‐SiC

Elastic constants for zinc‐blende AlN, GaN, and InN have been estimated from the elastic constants of the wurtzite phase. This has been accomplished by recognizing that the crystal structures of the wurtzite and zinc‐blende phases are related by a simple rotation. This rotation was then applied to the elastic constants and a least‐squares fit is used to match the results. Using the zinc‐blende elastic constants the critical thickness of the nitrides on β‐SiC substrates was calculated. The critical thickness of a single overlayer of AlN was calculated to be 14.1 nm, and for GaN the critical thickness was found to be 0.7 nm. In the elastic continuum model used there was no solution for the critical thickness of InN.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70563/2/JAPIAU-69-12-8423-1.pd

The role of surface tension in the growth of strained quantum wire arraysa)

The critical radius of a strained quantum wire and the potential strain stabilization of quantum wire arrays has been investigated for the InxGa1−xAs/GaAs system. The critical radius of the quantum wire was calculated using an energy balance approach. The wire was found to be more stable than the corresponding two‐dimensional quantum well structure. The use of surface tension as a stabilization force during the growth of strained quantum wire arrays is expected to have beneficial effects for arrays with greater than 7% InAs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70765/2/JAPIAU-69-2-717-1.pd

Time domain computational modelling of 1D arterial networks in monochorionic placentas

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Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations

One of the strengths of the discontinuous Galerkin (DG) method has been its balance between accuracy and robustness, which stems from DG’s intrinsic (upwind) dissipation being biased towards high frequencies/wavenumbers. This is particularly useful in high Reynolds-number flow simulations where limitations on mesh resolution typically lead to potentially unstable under-resolved scales. In continuous Galerkin (CG) discretisations, similar properties are achievable through the addition of artificial diffusion, such as spectral vanishing viscosity (SVV). The latter, although recognised as very useful in CG-based high-fidelity turbulence simulations, has been observed to be sub-optimal when compared to DG at intermediate polynomials orders (P ≈ 3). In this paper we explore an alternative stabilisation approach by the introduction of a continuous interior penalty on the gradient discontinuity at elemental boundaries, which we refer to as a gradient jump penalisation (GJP). Analogous to DG methods, this introduces a penalisation at the elemental interfaces as opposed to the interior element stabilisation of SVV. Detailed eigenanalysis of the GJP approach shows its potential as equivalent (sometimes superior) to DG dissipation and hence superior to previous SVV approaches. Through eigenanalysis, a judicious choice of GJP’s P-dependent scaling parameter is made and found to be consistent with previous apriori error analysis. The favourable properties of the GJP stabilisation approach are also supported by turbulent flow simulations of the incompressible Navier-Stokes equation, as we achieve high-quality flow solutions at P = 3 using GJP, whereas SVV performs marginally worse at P = 5 with twice as many degrees of freedom in total

Entanglement distribution for a practical quantum-dot-based quantum processor architecture

We propose a quantum dot (QD) architecture for enabling universal quantum information processing. Quantum registers, consisting of arrays of vertically stacked self-assembled semiconductor QDs, are connected by chains of in-plane self-assembled dots. We propose an entanglement distributor, a device for producing and distributing maximally entangled qubits on demand, communicated through in-plane dot chains. This enables the transmission of entanglement to spatially separated register stacks, providing a resource for the realization of a sizeable quantum processor built from coupled register stacks of practical size. Our entanglement distributor could be integrated into many of the present proposals for self-assembled QD-based quantum computation (QC). Our device exploits the properties of simple, relatively short, spin-chains and does not require microcavities. Utilizing the properties of self-assembled QDs, after distribution the entanglement can be mapped into relatively long-lived spin qubits and purified, providing a flexible, distributed, off-line resource. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft