An Arbitrary Lagrangian Eulerian Method for Three-Phase Flows with Triple Junction Points

We present a moving mesh method suitable for solving two-dimensional and axisymmetric three-liquid flows with triple junction points. This method employs a body-fitted unstructured mesh where the interfaces between liquids are lines of the mesh system, and the triple junction points (if exist) are mesh nodes. To enhance the accuracy and the efficiency of the method, the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally; dynamic boundary conditions on interfaces, in particular the triple points, are therefore incorporated naturally and accurately in a Finite- Element formulation. In order to allow pressure discontinuity across interfaces, double-values of pressure are necessary for interface nodes and triple-values of pressure on triple junction points. The resulting non-linear system of mass and momentum conservation is then solved by an Uzawa method, with the zero resultant condition on triple points reinforced at each time step. The method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid.

When is a symmetric body-hinge structure isostatic?

A symmetry-extended mobility rule is formulated for body-hinge frameworks and used to derive necessary symmetry conditions for isostatic (statically and kinematically indeterminate) frameworks. Constructions for symmetric body-hinge frameworks with an isostatic scalar count are reported, and symmetry counts are used to examine these structures for hidden, symmetry-detectable mechanisms. Frameworks of this type may serve as examples for exploration of a symmetry extension of the (now proven) 'molecular conjecture'. © 2014 Elsevier Ltd. All rights reserved.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.

An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.

3D Pose from Three Corresponding Points Under Weak-Perspective Projection

Model-based object recognition commonly involves using a minimal set of matched model and image points to compute the pose of the model in image coordinates. Furthermore, recognition systems often rely on the "weak-perspective" imaging model in place of the perspective imaging model. This paper discusses computing the pose of a model from three corresponding points under weak-perspective projection. A new solution to the problem is proposed which, like previous solutins, involves solving a biquadratic equation. Here the biquadratic is motivate geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which lead to a simple expression for the image position of any unmatched model point.

The topological behaviour of 3D null points in the Sun's corona

Brown D. S. and Priest E. R. 2001, The topological behaviour of 3D null points in the Sun's corona, Astronomy and Astrophysics, 367, 339-346

Contour Generator Points for Threshold Selection and a Novel Photo-Consistency Measure for Space Carving

Space carving has emerged as a powerful method for multiview scene reconstruction. Although a wide variety of methods have been proposed, the quality of the reconstruction remains highly-dependent on the photometric consistency measure, and the threshold used to carve away voxels. In this paper, we present a novel photo-consistency measure that is motivated by a multiset variant of the chamfer distance. The new measure is robust to high amounts of within-view color variance and also takes into account the projection angles of back-projected pixels. Another critical issue in space carving is the selection of the photo-consistency threshold used to determine what surface voxels are kept or carved away. In this paper, a reliable threshold selection technique is proposed that examines the photo-consistency values at contour generator points. Contour generators are points that lie on both the surface of the object and the visual hull. To determine the threshold, a percentile ranking of the photo-consistency values of these generator points is used. This improved technique is applicable to a wide variety of photo-consistency measures, including the new measure presented in this paper. Also presented in this paper is a method to choose between photo-consistency measures, and voxel array resolutions prior to carving using receiver operating characteristic (ROC) curves.

Evaluation of tumor response, disease control, progression-free survival, and time to progression as potential surrogate end points in metastatic breast cancer.

PURPOSE: Overall survival (OS) can be observed only after prolonged follow-up, and any potential effect of first-line therapies on OS may be confounded by the effects of subsequent therapy. We investigated whether tumor response, disease control, progression-free survival (PFS), or time to progression (TTP) could be considered a valid surrogate for OS to assess the benefits of first-line therapies for patients with metastatic breast cancer. PATIENTS AND METHODS: Individual patient data were collected on 3,953 patients in 11 randomized trials that compared an anthracycline (alone or in combination) with a taxane (alone or in combination with an anthracycline). Surrogacy was assessed through the correlation between the end points as well as through the correlation between the treatment effects on the end points. RESULTS: Tumor response (survival odds ratio [OR], 6.2; 95% CI, 5.3 to 7.0) and disease control (survival OR, 5.5; 95% CI, 4.8 to 6.3) were strongly associated with OS. PFS (rank correlation coefficient, 0.688; 95% CI, 0.686 to 0.690) and TTP (rank correlation coefficient, 0.682; 95% CI, 0.680 to 0.684) were moderately associated with OS. Response log ORs were strongly correlated with PFS log hazard ratios (linear coefficient [rho], 0.96; 95% CI, 0.73 to 1.19). Response and disease control log ORs and PFS and TTP log hazard ratios were poorly correlated with log hazard ratios for OS, but the confidence limits of rho were too wide to be informative. CONCLUSION: No end point could be demonstrated as a good surrogate for OS in these trials. Tumor response may be an acceptable surrogate for PFS.

Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Path-Dependency, Stocks, Switching Points, Flows: Reflections on Long-term Global Change and Local Opportunities

This paper examines the possibilities for peripheral localities to achieve upward mobility in the world-system by “hooking on” to larger processes of world-system accumulation. In particular, is it possible for economies that are dependent on foreign investment to receive a flow of investments that is high enough to overcome the negative impacts of a high stock of foreign investment, thus enabling them to cross a threshold and achieve upward mobility in the world-system? An analysis of therecent experience of the southern Irish “Celtic Tiger” economy during 1990-2000 indicates that such an upward movement is possible on the basis of massive foreign investment inflows. On closer examination, however, the Irish-type model appears to be highly deficient, because a high proportion of growth is illusionary and also on grounds of social desirability and lack of generalizability.