Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows

Applications of the DFLU flux to systems of conservation laws

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve systems of conservation laws. The obtained numerical flux is very close to a Godunov flux. As an example we consider a system modeling polymer flooding in oil reservoir engineering

Acoustic Tweezing and Patterning of Concentration Fields in Microfluidics

We demonstrate theoretically that acoustic forces acting on inhomogeneous fluids can be used to pattern and manipulate solute concentration fields into spatio-temporally controllable configurations stabilized against gravity. A theoretical framework describing the dynamics of concentration fields that weakly perturb the fluid density and speed of sound is presented and applied to study manipulation of concentration fields in rectangular-channel acoustic eigenmodes and in Bessel-function acoustic vortices. In the first example, methods to obtain horizontal and vertical multi-layer stratification of the concentration field at the end of a flow-through channel are presented. In the second example, we demonstrate acoustic tweezing and spatio-temporal manipulation of a local high-concentration region in a lower-concentration medium, thereby extending the realm of acoustic tweezing to include concentration fields.Comment: Revtex, 9 pages, 5 eps figure

The cardiac bidomain model and homogenization

We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface.Comment: To appear in Networks and Heterogeneous Media, Special Issue on Mathematical Methods for Systems Biolog

Forces acting on a small particle in an acoustical field in a thermoviscous fluid

We present a theoretical analysis of the acoustic radiation force on a single small particle, either a thermoviscous fluid droplet or a thermoelastic solid particle, suspended in a viscous and heat-conducting fluid medium. Our analysis places no restrictions on the length scales of the viscous and thermal boundary layer thicknesses $\delta_\mathrm{s}$ and $\delta_\mathrm{t}$ relative to the particle radius $a$, but it assumes the particle to be small in comparison to the acoustic wavelength $\lambda$. This is the limit relevant to scattering of sound and ultrasound waves from micrometer-sized particles. For particles of size comparable to or smaller than the boundary layers, the thermoviscous theory leads to profound consequences for the acoustic radiation force. Not only do we predict forces orders of magnitude larger than expected from ideal-fluid theory, but for certain relevant choices of materials, we also find a sign change in the acoustic radiation force on different-sized but otherwise identical particles. This phenomenon may possibly be exploited in handling of submicrometer-sized particles such as bacteria and vira in lab-on-a-chip systems.Comment: Revtex, 23 pages, 4 eps figure

Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds

We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be well-posed. We prove existence of generalized kinetic solutions using the vanishing viscosity method. A rigidity result is derived, which implies that generalized solutions are kinetic solutions and that kinetic solutions are uniquely determined by their initial data ($L^1$ contraction principle). Deprived of noise, the equations we consider coincide with those analyzed by Ben-Artzi and LeFloch (2007), who worked with Kruzkov-DiPerna solutions. In the Euclidian case, the stochastic equations agree with those examined by Debussche and Vovelle (2010).Comment: Submitted for publication on 23.09.1

Developments in Australian refugee law and policy (2012 to August 2013)

Introduction: This Research paper provides a snap-shot of significant developments in refugee law and policy during the period 2012 to August 2013 when the 43rd Parliament was prorogued and the House of Representatives dissolved for a general election. The commencement of 2012 saw the Government and Coalition remain at an impasse on offshore processing following the successful 2011 High Court challenge to the Government’s proposed Malaysia Arrangement. In the absence of bi-partisan support to implement statutory amendments to facilitate offshore processing, the Government began implementing a single visa processing framework for all asylum seekers which saw irregular maritime arrivals being processed in the same way as onshore protection visa applicants. That is, both began to be assessed under a statutory process with independent merits review by the Refugee Review Tribunal (RRT) and have equal access to judicial review of negative decisions. However, by mid-2012, the report of the Expert Panel on Asylum Seekers had been released and without delay, the Government begun implementing key recommendations, including the introduction of legislation to support the transfer of asylum seekers to regional processing countries, and creating capacity in Nauru and Papua New Guinea (PNG) to process asylum claims. The Government had also increased its Humanitarian Program to 20,000 places per year (with a minimum of 12,000 places being allocated for refugees), and it had removed family reunion concessions for proposers who had arrived through irregular maritime voyages. By the end of 2012, the Government had also begun implementing the Expert Panel’s ill-defined ‘no advantage’ principle to prevent boat arrivals benefitting from circumventing regular migration arrangements. It implemented this principle by selecting and transferring some boat arrivals to the regional processing centres in PNG and Nauru. The principle was also applied to an increasing number of asylum seekers released into the community on the mainland on bridging visas by denying them the opportunity to work and offering them only limited financial support. Significantly, these boat arrivals also remained ineligible for the grant of protection visas ‘until such time that they would have been resettled in Australia after being processed in our region’. However, the Government never clarified the number of years it envisaged these asylum seekers would wait for final resolution of their status, nor did it rule out the possibility of sending them offshore at a later date. The Government subsequently estimated that some 19,000 asylum seekers living in the community were subject to the ‘no advantage’ principle. Two months before the 2013 federal election and in the wake of growing support for the Opposition’s tougher border protection policies, newly appointed Prime Minister, Kevin Rudd made a surprise announcement on 19 July 2013 that Australia had entered into a Regional Resettlement Arrangement with PNG. Under the Arrangement, all asylum seekers that henceforth arrive by boat would be liable for transfer to PNG for processing and resettlement in PNG and in any other participating regional State. He subsequently makes a similar Memorandum of Understanding (MOU) with Nauru. Notwithstanding the Government’s policy shift, the Australian Labor Party was unable to secure another term in office and on 7 September 2013, the Liberal and National parties were voted in to form a Coalition Government, led by Tony Abbott. This paper provides a brief chronology of these and other significant events during the reporting period. It also outlines key legal developments by examining significant Federal and High Court judgments and provides a brief overview of the Bills that were introduced. The paper also briefly examines key policy developments and provides an overview of significant reports and parliamentary inquiries finalised during the reporting period. In doing so, this paper builds upon previous Parliamentary Library publications, Developments in Australian refugee law and policy 2010—2011 and Developments in Australian refugee law and policy 2007–10: Labor’s first term in office