Calibration of the length of a chain of single gold atoms

Using a scanning tunnelling microscope or mechanically controllable break junction it has been shown that it is possible to control the formation of a wire made of single gold atoms. In these experiments an interatomic distance between atoms in the chain of ∼3.6 Å was reported which is not consistent with recent theoretical calculations. Here, using precise calibration procedures for both techniques, we measure the length of the atomic chains. Based on the distance between the peaks observed in the chain length histogram we find the mean value of the interatomic distance before chain rupture to be 2.5±0.2 Å. This value agrees with the theoretical calculations for the bond length. The discrepancy with the previous experimental measurements was due to the presence of He gas, that was used to promote the thermal contact, and which affects the value of the work function that is commonly used to calibrate distances in scanning tunnelling microscopy and mechanically controllable break junctions at low temperatures.

Portable 3D laser-camera calibration system with color fusion for SLAM

Nowadays, the use of RGB-D sensors have focused a lot of research in computer vision and robotics. These kinds of sensors, like Kinect, allow to obtain 3D data together with color information. However, their working range is limited to less than 10 meters, making them useless in some robotics applications, like outdoor mapping. In these environments, 3D lasers, working in ranges of 20-80 meters, are better. But 3D lasers do not usually provide color information. A simple 2D camera can be used to provide color information to the point cloud, but a calibration process between camera and laser must be done. In this paper we present a portable calibration system to calibrate any traditional camera with a 3D laser in order to assign color information to the 3D points obtained. Thus, we can use laser precision and simultaneously make use of color information. Unlike other techniques that make use of a three-dimensional body of known dimensions in the calibration process, this system is highly portable because it makes use of small catadioptrics that can be placed in a simple manner in the environment. We use our calibration system in a 3D mapping system, including Simultaneous Location and Mapping (SLAM), in order to get a 3D colored map which can be used in different tasks. We show that an additional problem arises: 2D cameras information is different when lighting conditions change. So when we merge 3D point clouds from two different views, several points in a given neighborhood could have different color information. A new method for color fusion is presented, obtaining correct colored maps. The system will be tested by applying it to 3D reconstruction.

Portable 3D laser-camera calibration system with color fusion for SLAM

Paper submitted to the 43rd International Symposium on Robotics (ISR2012), Taipei, Taiwan, Aug. 29-31, 2012.

Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.

Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty

In this work, we analyze the effect of demand uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear program (MILP) with the unique feature of incorporating explicitly the demand uncertainty using scenarios with given probability of occurrence. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact.

High-Resolution N2 Adsorption Isotherms at 77.4 K: Critical Effect of the He Used During Calibration

Accurate characterization of the microporous structure in porous solids is of paramount importance for several applications such as energy and gas storage, nanoconfinement reactions, and so on. Among the different techniques for precise textural characterization, high-precision gas adsorption measurement of probe molecules at cryogenic temperatures (e.g., N2 at 77.4 K and Ar at 87.3 K) is the most widely used, after appropriate calibration of the sample holder with a probe gas, which does not experience physisorption processes. Although traditionally helium has been considered not to be adsorbed in porous solids at cryogenic temperatures, here we show that even at 77.4 K (high above its boiling temperature, 4 K) the use of He in the calibration step can give rise to erroneous interpretations when narrow micropores/constrictions are present.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

The multiobjective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently, we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.