Early detection of ageing in solder joints through laser probe thermal analysis of the peltier effect

We have recently developed an optical contactless method for testing the quality of solder joints during accelerated thermal cycling ageing processes.¹ The method was based upon the measurement of the dynamic thermal behaviour of the joint to short bursts of Joule heating. It has proved to be efficient in revealing the formation of cracks at the lead-solder interface. We present a method to evaluate ageing at a much earlier stage in the cycling process. We have observed in earlier work,¹ that before cracks appear, structural changes occur in the solder at the lead-solder interface. The thermal response of the solder joint is recorded over time to a Peltier heat perturbation produced by flowing a current pulse through the interface where structural changes occur. The key point in this method is to discriminate the Peltier effect from the Joule thermal response because both effects generate heat. The variation of the early Peltier response in the thermal cycling ageing tests is seen as a quantitative signature of the structural changes in the lead-solder interface.     

Terrain Modelling from Feature Primitives

We introduce a compact hierarchical procedural model that combines feature‐based primitives to describe complex terrains with varying level of detail. Our model is inspired by skeletal implicit surfaces and defines the terrain elevation function by using a construction tree. Leaves represent terrain features and they are generic parametrized skeletal primitives, such as mountains, ridges, valleys, rivers, lakes or roads. Inner nodes combine the leaves and subtrees by carving, blending or warping operators. The elevation of the terrain at a given point is evaluated by traversing the tree and by combining the contributions of the primitives. The definition of the tree leaves and operators guarantees that the resulting elevation function is Lipschitz, which speeds up the sphere tracing used to render the terrain. Our model is compact and allows for the creation of large terrains with a high level o detail using a reduced set of primitives. We show the creation of different kinds of landscapes and demonstrate that our model allows to efficiently control the shape and distribution of landform features.     

Modular Composition Modulo Triangular Sets and Applications

We generalize Kedlaya and Umans’ modular composition algorithm to the multivariate case. As a main application, we give fast algorithms for many operations involving triangular sets (over a finite field), such as modular multiplication, inversion, or change of order. For the first time, we are able to exhibit running times for these operations that are almost linear, without any overhead exponential in the number of variables. As a further application, we show that, from the complexity viewpoint, Charlap, Coley, and Robbins’ approach to elliptic curve point counting can be competitive with the better known approach due to Elkies.     

Flow modeling of linear and nonlinear fluids in two scale fibrous fabrics

The fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium is the permeability. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. As permeability reflects both the magnitude and anisotropy of the fluid/fiber resistance, efficient numerical techniques are needed to solve linear and nonlinear homogenization problems online during the flow simulation. In a previous work the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and rheo-thinning resins. In the linear case only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as representative microscopic volumes exist in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, microscopic calculation must be carried out many times because the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. Thus, a nonlinear multi-scale problem results. In this paper an original and efficient offline-online procedure is proposed for the efficient solution of nonlinear flow problems in porous media.     

Vademecum‐based GFEM (V‐GFEM): optimal enrichment for transient problems

This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.     

Multi-contact vertical ladder climbing with an HRP-2 humanoid

We describe the research and the integration methods we developed to make the HRP-2 humanoid robot climb vertical industrial-norm ladders. We use our multi-contact planner and multi-objective closed-loop control formulated as a QP (quadratic program). First, a set of contacts to climb the ladder is planned off-line (automatically or by the user). These contacts are provided as an input for a finite state machine. The latter builds supplementary tasks that account for geometric uncertainties and specific grasps procedures to be added to the QP controller. The latter provides instant desired states in terms of joint accelerations and contact forces to be tracked by the embedded low-level motor controllers. Our trials revealed that hardware changes are necessary, and parts of software must be made more robust. Yet, we confirmed that HRP-2 has the kinematic and power capabilities to climb real industrial ladders, such as those found in nuclear power plants and large scale manufacturing factories (e.g. aircraft, shipyard) and construction sites.     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

Good reduction of Puiseux series and applications

We have designed a new symbolic-numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well-chosen prime number p are used to obtain the exact information needed to guide floating point computations. In this paper, we detail the symbolic part of our algorithm. First of all, we study modular reduction of Puiseux series and give a good reduction criterion for ensuring that the information required by the numerical part is preserved. To establish our results, we introduce a simple modification of classical Newton polygons, that we call “generic Newton polygons”, which turns out to be very convenient. Finally, we estimate the size of good primes obtained with deterministic and probabilistic strategies. Some of these results were announced without proof at ISSAC’08.     

Imaging biofilm in porous media using X-ray computed microtomography

In this study, a new technique for three-dimensional imaging of biofilm within porous media using X-ray computed microtomography is presented. Due to the similarity in X-ray absorption coefficients for the porous media (plastic), biofilm and aqueous phase, an X-ray contrast agent is required to image biofilm within the experimental matrix using X-ray computed tomography. The presented technique utilizes a medical suspension of barium sulphate to differentiate between the aqueous phase and the biofilm. Potassium iodide is added to the suspension to aid in delineation between the biofilm and the experimental porous medium. The iodide readily diffuses into the biofilm while the barium sulphate suspension remains in the aqueous phase. This allows for effective differentiation of the three phases within the experimental systems utilized in this study. The behaviour of the two contrast agents, in particular of the barium sulphate, is addressed by comparing two-dimensional images of biofilm within a pore network obtained by (1) optical visualization and (2) X-ray absorption radiography. We show that the contrast mixture provides contrast between the biofilm, the aqueous-phase and the solid-phase (beads). The imaging method is then applied to two three-dimensional packed-bead columns within which biofilm was grown. Examples of reconstructed images are provided to illustrate the effectiveness of the method. Limitations and applications of the technique are discussed. A key benefit, associated with the presented method, is that it captures a substantial amount of information regarding the topology of the pore-scale transport processes. For example, the quantification of changes in porous media effective parameters, such as dispersion or permeability, induced by biofilm growth, is possible using specific upscaling techniques and numerical analysis. We emphasize that the results presented here serve as a first test of this novel approach; issues with accurate segmentation of the images, optimal concentrations of contrast agents and the potential need for use of synchrotron radiation sources need to be addressed before the method can be used for precise quantitative analysis of biofilm geometry in porous media.