Analysis of a finite element formulation for modelling phase separation

In Combescure, A., De Borst, R., and Belytschko, T., editors, IUTAM Symposium on Discretization Methods for Evolving Discontinuities, volume 5 of IUTAM Bookseries, pages 89–102. Springer.The Cahn-Hilliard equation is of importance in materials science and a range of other fields. It represents a diffuse interface model for simulating the evolution of phase separation in solids and fluids, and is a nonlinear fourth-order parabolic equation, which makes its numerical solution particularly challenging. To this end, a finite element formulation has been developed which can solve the Cahn-Hilliard equation in its primal form using C^0 basis functions. Here, analysis of a fully discrete version of this method is presented in the form of a priori uniqueness, stability and error analysis

Evaluation of a pulsed ultrasonic Doppler flowmeter

The in vivo application of the pulsed ultrasound Doppler velocity meter (PUDVM) for measuring arterial velocity waveforms is reported. In particular, the performance of the PUDVM is compared with a hot film anemometer of proven accuracy

Formulation of continuous/discontinuous Galerkin methods for strain gradient-dependent damage

Continuum damage models are widely used to represent the development of microscopic defects that coalesce into a macroscopic crack. The microscopic defects cause a progressive weakening or softening of the material (damage). Strain gradient-dependent terms have been included in some damage theories to regularize them, and thereby avoid a pathological mesh-dependence in the solution. A strain gradient-dependent damage model is considered here for the simulation of this feature in quasi-brittle materials. In the model considered, the damage parameter depends upon a regularized equivalent strain. The regularization is introduced through a dependency on the Laplacian of an equivalent strain measure. The introduction of the Laplacian of the strain leads to numerical difficulties as the governing differential equations are fourth-order, and additional boundary conditions must be specified. The application of such a model in a standard finite element framework requires $C^1$ continuity of the shape functions. Here, a continuous/discontinuous mixed Galerkin method is presented which avoids the need for high-order continuity. The formulation allows the use of $C^0$ or $C^{-1}$ interpolations for the regularized strain field and a $C^0$ interpolation of the displacement field. Numerical examples are presented to validate the formulation in one and two dimensions. Several interpolations are tested extensively in one dimension in order to provide guidance for the most appropriate formulations in two dimensions. The formulation is applied to crack propagation in a three-point bending test, with the computed result being independent of the discretization

A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model: 2D results

The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models which involve gradients of the strain eld means that the $C^0$ continuity of standard nite element shape functions is insu cient. In this work, a continuous/discontinuous Galerkin formulation is developed to solve a strain gradient-dependent damage problem in a rigorous manner. Potential discontinuities in the strain field across element boundaries are incorporated in the weak form of the governing equations. The performance of the formulation is tested in one dimension for various interpolations, which provides guidance for two-dimensional simulations

AUTOTEM - Automated geometry meshing and heat conduction calculation

Temperature distribution for an arbitrary irregular body is calculated by AUTOTEM, which generates required input data automatically by computer. Temperature distribution is calculated for a two-dimensional plane section in /x,y/ coordinates or for an axisymmetric irregular body in /r,z/ coordinates

Three small transiting planets around the M dwarf host star LP 358-499

We report on the detection of three transiting small planets around the low-mass star LP 358-499 (K2-133), using photometric data from the Kepler-K2 mission. Using multiband photometry, we determine the host star to be an early M dwarf with an age likely older than a Gigayear. The three detected planets K2-133 b, c, and d have orbital periods of ca. 3, 4.9 and 11 days and transit depths of ca. 700, 1000 and 2000 ppm, respectively. We also report a planetary candidate in the system (EPIC 247887989.01) with a period of 26.6 days and a depth of ca. 1000 ppm, which may be at the inner edge of the stellar habitable zone, depending on the specific host star properties. Using the transit parameters and the stellar properties, we estimate that the innermost planet may be rocky. The system is suited for follow-up observations to measure planetary masses and JWST transmission spectra of planetary atmospheres.Comment: Accepted for publication in MNRAS Letters. Replaced previous arXiv version with final submitted versio

Validation of a Temperate Fourth Planet in the K2-133 Multi-planet System

We present follow-up observations of the K2-133 multi-planet system. Previously, we announced that K2-133 contained three super-Earths orbiting an M1.5V host star - with tentative evidence of a fourth outer-planet orbiting at the edge of the temperate zone. Here we report on the validation of the presence of the fourth planet, determining a radius of $1.73_{-0.13}^{+0.14}$ R$_{\oplus}$. The four planets span the radius gap of the exoplanet population, meaning further follow-up would be worthwhile to obtain masses and test theories of the origin of the gap. In particular, the trend of increasing planetary radius with decreasing incident flux in the K2-133 system supports the claim that the gap is caused by photo-evaporation of exoplanet atmospheres. Finally, we note that K2-133 e orbits on the edge of the stars temperate zone, and that our radius measurement allows for the possibility that this is a rocky world. Additional mass measurements are required to confirm or refute this scenario.Comment: Accepted for publication in MNRA

SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio

Temporal markers of prosodic boundaries in children's speech production

It is often thought that the ability to use prosodic features accurately is mastered in early childhood. However, research to date has produced conflicting evidence, notably about the development of children's ability to mark prosodic boundaries. This paper investigates (i) whether, by the age of eight, children use temporal boundary features in their speech in a systematic way, and (ii) to what extent adult listeners are able to interpret their production accurately and unambiguously. The material consists of minimal pairs of utterances: one utterance includes a compound noun, in which there is no prosodic boundary after the first noun, e.g. ‘coffee-cake and tea’, while the other utterance includes simple nouns, separated by a prosodic boundary, e.g. ‘coffee, cake and tea’. Ten eight-year-old children took part, and their productions were rated by 23 adult listeners. Two phonetic exponents of prosodic boundaries were analysed: pause duration and phrase-final lengthening. The results suggest that, at the age of 8, there is considerable variability among children in their ability to mark phrase boundaries of the kind analysed in the experiment, with some children failing to differentiate between the members of the minimal pairs reliably. The differences between the children in their use of boundary features were reflected in the adults' perceptual judgements. Both temporal cues to prosodic boundaries significantly affected the perceptual ratings, with pause being a more salient determinant of ratings than phrase-final lengthening