Understanding the formation of twinned dendrites (‘feather’ grains)

The phenomenon of feather grain growth is interesting from both a theoretical and commercial point of view. Here we report the results of phase-field simulations aimed at understanding the formation of twinned dendrites. We show that, while a competition between oppositely directed capillary and kinetic anisotropies with a simple four-fold symmetry can produce low anisotropy structures such as dendritic seaweed, there is no indication that this can give rise to twinned dendrites. In contrast, adding small components of an anisotropy, with higher order harmonics, can produce features reminiscent of twinned dendrites and may also be able to stabilise the grooved tip morphology

Reframing Libel - Taking All Rights Seriously and where it leads us

In preparing this paper, we have returned to first principles and re-evaluated fundamental aspects of libel law, its purposes, its substance, and its processes. Our thinking has been informed by, first, philosophical understandings of democracy and the public sphere and in particular the role of freedom of speech and of the media therein, and secondly, the social psychology of reputation and privacy. By doing this, we are able to ground some of the proposals for reform made previously by Index on Censorship, English PEN, Lord Lester, and others. We do so, however, not through the prism of an over-weaned emphasis on freedom of expression, but rather by triangulating the rights and interests of claimants, defendants, and the wider public. Ultimately, we recommend a coherent set of significant substantive and procedural reforms that if enacted would enhance access to justice and reduce costs for all but the most serious and/or most damaging libels. This involves the recommendation of the introduction of a two-track libel regim

Heat transfer studies of solid rocket igniters quarterly progress report no. 3

Heat transfer of solid rocket igniters - flow visualization tests, copper tube firing, and radiant heat transfer analysi

A fully implicit, fully adaptive time and space discretisation method for phase-field simulation of binary alloy solidification

A fully-implicit numerical method based upon adaptively refined meshes for the simulation of binary alloy solidification in 2D is presented. In addition we combine a second-order fully-implicit time discretisation scheme with variable steps size control to obtain an adaptive time and space discretisation method. The superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, is shown. Due to the high non-linearity of the governing equations a robust and fast solver for systems of nonlinear algebraic equations is needed to solve the intermediate approximations per time step. We use a nonlinear multigrid solver which shows almost h-independent convergence behaviour

An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal solidification of a dilute binary alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ*, was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant

Advanced numerical methods for the simulation of alloy solidification with high Lewis number

A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems of non-linear algebraic equations is used to solve the intermediate approximations per time step. For the isothermal case, the superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, has been demonstrated and published previously. Here, the new proposed method has been applied to the thermalsolutal case with high Lewis number, where stability issues and time step restrictions have been major constraints in previous research

ICF core sets for low back pain: do they include what matters to patients?

To investigate whether the International Classification of Functioning Disability and Health (ICF) Core Sets for low back pain encompass the key functional problems of patients

A phase-field model for the diffusive melting of isolated dendritic fragments

A thermal phase-field model constructed in the "thin-interface" limit and incorporating a number of advanced numerical techniques such as adaptive mesh refinement, implicit time stepping, and a multigrid solver has been used to study the isolated diffusive melting of dendritic fragments. The results of the simulations are found to be fully consistent with the experimental observation of such melting in microgravity during the Isothermal Dendrite Growth Experiment. It is found that the rate at which the ratio of semi-major to semi-minor axes changes is a function of the melt Stefan number, which may help explain why both melting at (approximately) constant ratio and melting at slowly increasing ratio have been observed