Multiscale modelling methodologies build macroscale models of materials with complicated fine microscale structure. We propose a methodology to derive boundary conditions for the macroscale model of a prototypical non-linear heat exchanger. The deriv
ed macroscale boundary conditions improve the accuracy of macroscale model. We verify the new boundary conditions by numerical methods. The techniques developed here can be adapted to a wide range of multiscale reaction-diffusion-advection systems.
Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must be develo
ped which minimise the transfer of data. Patch dynamics is a computational macroscale modelling scheme which provides a coarse macroscale solution of a problem defined on a fine microscale by dividing the domain into many nonoverlapping, coupled patches. Patch dynamics is readily adaptable to massive parallelisation as each processor can evaluate the dynamics on one, or a few, patches. However, patch coupling conditions interpolate across the unevaluated parts of the domain between patches, and are typically reevaluated at every microscale time step, thus requiring almost continuous data transfer. We propose a modified patch dynamics scheme which minimises data transfer by only reevaluating the patch coupling conditions at `mesoscale time scales which are significantly larger than the microscale time of the microscale problem. We analyse the error arising from patch dynamics with mesoscale temporal coupling as a function of the mesoscale time interval, patch size, and ratio between the microscale and macroscale.
Modern technology unintentionally provides resources that enable the trust of everyday interactions to be undermined. Some authentication schemes address this issue using devices that give unique outputs in response to a challenge. These signatures a
re generated by hard-to-predict physical responses derived from structural characteristics, which lend themselves to two different architectures, known as unique objects (UNOs) and physically unclonable functions (PUFs). The classical design of UNOs and PUFs limits their size and, in some cases, their security. Here we show that quantum confinement lends itself to the provision of unique identities at the nanoscale, by using fluctuations in tunnelling measurements through quantum wells in resonant tunnelling diodes (RTDs). This provides an uncomplicated measurement of identity without conventional resource limitations whilst providing robust security. The confined energy levels are highly sensitive to the specific nanostructure within each RTD, resulting in a distinct tunnelling spectrum for every device, as they contain a unique and unpredictable structure that is presently impossible to clone. This new class of authentication device operates with few resources in simple electronic structures above room temperature.
We present an experimentally guided, multi-phasic, multi-species ionic gel model to compare and make qualitative predictions on the rheology of mucus of healthy individuals (Wild Type) versus those infected with Cystic Fibrosis. The mixture theory co
nsists of the mucus (polymer phase) and water (solvent phase) as well as several different ions: H+, Na+ and Ca++. The model is linearized to study the hydration of spherically symmetric mucus gels and calibrated against the experimental data of mucus diffusivities. Near equilibrium, the linearized form of the equation describing the radial size of the gel, reduces to the well-known expression used in the kinetic theory of swelling hydrogels. Numerical studies reveal that the Donnan potential is the dominating mechanism driving the mucus swelling/deswelling transition. However, the altered swelling kinetics of the Cystic Fibrosis infected mucus is not merely governed by the hydroelectric composition of the swelling media, but also due to the altered movement of electrolytes as well as due to the defective properties of the mucin polymer network.
Modelling sediment transport in environmental turbulent fluids is a challenge. This article develops a sound model of the lateral transport of suspended sediment in environmental fluid flows such as floods and tsunamis. The model is systematically de
rived from a 3D turbulence model based on the Smagorinski large eddy closure. Embedding the physical dynamics into a family of problems and analysing linear dynamics of the system, centre manifold theory indicates the existence of slow manifold parametrised by macroscale variables. Computer algebra then constructs the slow manifold in terms of fluid depth, depth-averaged lateral velocities, and suspended sediment concentration. The model includes the effects of sediment erosion, advection, dispersion, and also the interactions between the sediment and turbulent fluid flow. Vertical distributions of the velocity and concentration in steady flow agree with the established experimental data. Numerical simulations of the suspended sediment under large waves show that the developed model predicts physically reasonable phenomena.
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differentialdifference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements empowers the
approach to resolve significant subgrid microscale structures and interactions between neighbouring elements. The crucial aspect of this approach is that centre manifold theory organises the resolution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements. The techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differentialdifference equations, such as the forced Burgers equation, adopted here as an illustrative example.
We consider one dimensional lattice diffusion model on a microscale grid with many discrete diffusivity values which repeat periodicially. Computer algebra explores how the dynamics of small coupled `patches predict the slow emergent macroscale dynam
ics. We optimise the geometry and coupling of patches by comparing the macroscale predictions of the patch solutions with the macroscale solution on the infinite domain, which is derived for a general diffusivity period. The results indicate that patch dynamics is a viable method for numerical macroscale modelling of microscale systems with fine scale roughness. Moreover, the minimal error on the macroscale is generally obtained by coupling patches via `buffers that are as large as half of each patch.
We describe and report first results from PALM-3000, the second-generation astronomical adaptive optics facility for the 5.1-m Hale telescope at Palomar Observatory. PALM-3000 has been engineered for high-contrast imaging and emission spectroscopy of
brown dwarfs and large planetary mass bodies at near-infrared wavelengths around bright stars, but also supports general natural guide star use to V ~ 17. Using its unique 66 x 66 actuator deformable mirror, PALM-3000 has thus far demonstrated residual wavefront errors of 141 nm RMS under 1 arcsecond seeing conditions. PALM-3000 can provide phase conjugation correction over a 6.4 x 6.4 arcsecond working region at an observing wavelength of 2.2 microns, or full electric field (amplitude and phase) correction over approximately one half of this field. With optimized back-end instrumentation, PALM-3000 is designed to enable as high as 10e-7 contrast at ~1 arc second angular separation, after including post-observation speckle suppression processing. While optimization of the adaptive optics system is ongoing, we have already successfully commissioned five back-end science instruments and begun a major exoplanet characterization survey, Project 1640, with our partners at American Museum of Natural History and Jet Propulsion Laboratory.
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is dynamically att
ractive, and if it is, to what particular solution does the system evolve. By recasting a class of stochastic PDEs in a form to which stochastic centre manifold theory may be applied we resolve these issues in this class. For definiteness, a first example of self-similarity of the Burgers equation driven by some stochastic forced is studied. Under suitable assumptions, a stationary solution is constructed which yields the existence of a stochastic self-similar solution for the stochastic Burgers equation. Furthermore, the asymptotic convergence to the self-similar solution is proved. Second, in more general stochastic reaction-diffusion systems stochastic centre manifold theory provides a framework to construct the similarity solution, confirm its relevance, and determines the correct solution for any compact initial condition. Third, we argue that dynamically moving the spatial origin and dynamically stretching time improves the description of the stochastic similarity. Lastly, an application to an extremely simple model of turbulent mixing shows how anomalous fluctuations may arise in eddy diffusivities. The techniques and results we discuss should be applicable to a wide range of stochastic similarity problems.
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations u u_{tt}+u_t=D u+f(u)+ u^alphadot{W} on a bounded spatial domain. An asymptoti
c approximation to the stochastic wave equation is constructed by a special transformation and splitting of $ u u_{t}$. This splitting gives a clear description of the structure of $u$. The approximating model, for small $ u>0$,, is a stochastic nonlinear heat equation for exponent $0leqalpha<1$,, and is a deterministic nonlinear wave equation for exponent $alpha>1$,.
