Preliminary investigations of weak non-adiabatic effects in materials from simulations on model clusters

According to earlier work, excited electronic states, despite their very small concentrations in wide-gap systems, might be involved in the initiation of energetic materials. To get further insight into the non-adiabatic electronic behaviour under intense mechanical perturbations, a simple approach is suggested, using finite clusters as models for materials. Preliminary calculations are carried out for isolated clusters undergoing vibrations. Electronic populations in excited states obtained from these simulations are much larger than expected on the basis of statistical mechanics. Therefore, an extension of the present scheme to the canonical NVT ensemble would be desirable.     

Characterization of PVA cryogel for intravascular ultrasound elasticity imaging

The present study characterizes the mechanical properties of polyvinyl alcohol (PVA) cryogel in order to show its utility for intravascular elastography. PVA cryogel becomes harder with an increasing number of freeze-thaw cycles, and Young's modulus and Poisson's ratio are measured for seven samples. Mechanical tests were performed on cylindrical samples with a pressure column and on a hollow cylinder with the calculation of an intravascular elastogram. An image of the Young's modulus was obtained from the elastogram using cylinder geometry properties. Results show the mechanical similitude of PVA cryogel with the biological tissues present in arteries. A good agreement between Young's modulus obtained from pressure column and from elastogram was also observed.     

Globally Optimal Estimates for Geometric Reconstruction Problems

We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality—or a combination of both—we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.     

Credible autocoding of convex optimization algorithms

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety-critical roles. There is a considerable body of mathematical proofs on on-line optimization algorithms which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks on how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be addressed in future work.     

Trajectory planning/re-planning for satellite systems in rendezvous mission in the presence of actuator faults based on attainable efforts analysis

The objective of fault-tolerant control (FTC) is to minimise the effect of faults on system performance (stability, trajectory tracking, etc.). However, the majority of the existing FTC methods continue to force the system to follow the pre-fault trajectories without considering the reduction in available control resources caused by actuator faults. Forcing the system to follow the same trajectories as before fault occurrence may result in actuator saturation and system's instability. Thus, pre-fault objectives should be redefined in function of the remaining resources to avoid potential saturation. The main contribution of this paper is a flatness-based trajectory planning/re-planning method that can be combined with any active FTC approach. The work considers the case of over-actuated systems where a new idea is proposed to evaluate the severity of faults occurred. In addition, the trajectory planning/re-planning approach is formulated as an optimisation problem based on the analysis of attainable efforts domain in fault-free and fault cases. The proposed approach is applied to two satellite systems in rendezvous mission.     

Packing spherical discrete elements for large scale simulations

We introduce a new geometric method to generate sphere packings with restricted overlap values. Sample generation is an important, but time-consuming, step that precedes a calculation performed with the discrete element method (DEM). At present, there does not exist any software dedicated to DEM which would be similar to the mesh software that exists for finite element methods (FEM). A practical objective of the method is to build very large sphere packings (several hundreds of thousands) in a few minutes instead of several days as the current dynamic methods do. The developed algorithm uses a new geometric procedure to position very efficiently the polydisperse spheres in a tetrahedral mesh. The algorithm, implemented into YADE-OPEN DEM (open-source software), consists in filling tetrahedral meshes with spheres. In addition to the features of the tetrahedral mesh, the input parameters are the minimum and maximum radii (or their size ratio), and the magnitude of authorized overlaps. The filling procedure is stopped when a target solid fraction or number of spheres is reached. Based on this method, an efficient tool can be designed for DEMs used by researchers and engineers. The generated packings can be isotropic and the number of contacts per sphere is very high due to its geometric procedure. In this paper, different properties of the generated packings are characterized and examples from real industrial problems are presented to show how this method can be used. The current C++ version of this packing algorithm is part of YADE-OPEN DEM [20] available on the web (https://yade-dem.org).     

A fuzzy constraint-based approach to data reconciliation in material flow analysis

Data reconciliation consists in modifying noisy or unreliable data in order to make them consistent with a mathematical model (herein a material flow network). The conventional approach relies on least-squares minimization. Here, we use a fuzzy set-based approach, replacing Gaussian likelihood functions by fuzzy intervals, and a leximin criterion. We show that the setting of fuzzy sets provides a generalized approach to the choice of estimated values, that is more flexible and less dependent on oftentimes debatable probabilistic justifications. It potentially encompasses interval-based formulations and the least squares method, by choosing appropriate membership functions and aggregation operations. This paper also lays bare the fact that data reconciliation under the fuzzy set approach is viewed as an information fusion problem, as opposed to the statistical tradition which solves an estimation problem.