WIMU instrumentation of assassin trainer & skeleton sled – initial data capture

Science Foundation Ireland (CSET - Centre for Science, Engineering and Technology, Grant No. 07/CE/11147)

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of solutions for the 3D-micropolar fluid system with initial data in Besov-Morrey spaces

In this paper, we show a local-in-time existence result for the 3D micropolar fluid system in the framework of Besov-Morrey spaces. The initial data class is larger than the previous ones and contains strongly singular functions and measures. © 2013 Springer Basel.

Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

Quenching phenomenon of singular parabolic problems with L1 initial data

We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that L1 Ω is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L1-initial datum.

General revenue sharing: initial state & local data elements.

Cover title.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

(Table T4) Final depth vs. velocity and two-way traveltime data, ODP Site 178-1103

Site 1103 was one of a transect of three sites drilled across the Antarctic Peninsula continental shelf during Leg 178. The aim of drilling on the shelf was to determine the age of the sedimentary sequences and to ground truth previous interpretations of the depositional environment (i.e., topsets and foresets) of progradational seismostratigraphic sequences S1, S2, S3, and S4. The ultimate objective was to obtain a better understanding of the history of glacial advances and retreats in this west Antarctic margin. Drilling the topsets of the progradational wedge (0-247 m below seafloor [mbsf]), which consist of unsorted and unconsolidated materials of seismic Unit S1, was very unfavorable, resulting in very low (2.3%) core recovery. Recovery improved (34%) below 247 mbsf, corresponding to sediments of seismic Unit S3, which have a consolidated matrix. Logs were only obtained from the interval between 75 and 244 mbsf, and inconsistencies on the automatic analog picking of the signals received from the sonic log at the array and at the two other receivers prevented accurate shipboard time-depth conversions. This, in turn, limited the capacity for making seismic stratigraphic interpretations at this site and regionally. This study is an attempt to compile all available data sources, perform quality checks, and introduce nonstandard processing techniques for the logging data obtained to arrive at a reliable and continuous depth vs. velocity profile. We defined 13 data categories using differential traveltime information. Polynomial exclusion techniques with various orders and low-pass filtering reduced the noise of the initial data pool and produced a definite velocity depth profile that is synchronous with the resistivity logging data. A comparison of the velocity profile produced with various other logs of Site 1103 further validates the presented data. All major logging units are expressed within the new velocity data. A depth-migrated section with the new velocity data is presented together with the original time section and initial depth estimates published within the Leg 178 Initial Reports volume. The presented data confirms the location of the shelf unconformity at 222 ms two-way traveltime (TWT), or 243 mbsf, and allows its seismic identification as a strong negative and subsequent positive reflection.

Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

Comparison of below-knee amputee gait performed overground and on a motorized treadmill

There has been no direct attempt to evaluate whether gait performed overground and on a treadmill is the same for lower limb amputees. A multiple case study approach was adopted to explore the degenerate movement behavior displayed by three male amputees. Participants walked overground at a self-selected preferred pace and when this speed was enforced on a treadmill (50 stride cycles per condition). The extremities of motion (i.e., maximum flexion) for the hip and knee joints differed between conditions (0.2–3.8°). For two participants, the temporal asymmetry of gait was reduced on the treadmill. Initial data suggest that research on amputees simulating overground walking on a treadmill might need to be interpreted with some caution.