Isogeometric Analysis on V-reps: first results

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio

On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics

International audienceThis article adresses the delicate issue of estimating physical uncertainties in aerodynamics. Usually, flow simulations are performed in a fully deterministic approach, although in real life operational uncertainty arises due to unpredictable factors that alter the flow conditions. In this article, we present and compare two methods to account for uncertainty in aerodynamic simulation. Firstly, automatic differentiation tools are used to estimate first- and second-order derivatives of aerodynamic coefficients with respect to uncertain variables, yielding an estimate of expectation and variance values (Method of Moments). Secondly, metamodelling techniques (radial basis functions, kriging) are employed in conjunction with Monte-Carlo simulations to derive statistical information. These methods are demonstrated for 3D Eulerian flows around the wing of a business aircraft at different regimes subject to uncertain Mach number and angle of attack

Sensitivity Evaluation in Aerodynamic Optimal Design

The possibility to compute first- and second-derivatives of functionals subject to equality constraints given by state equations (and in particular non-linear systems of Partial Derivative Equations) allows us to use efficient techniques to solve several industrial-strength problems. Among possible applications that require knowledge of the derivatives, let us mention: aerodynamic shape optimization with gradient-based descent algorithms, propagation of uncertainties using perturbation techniques, robust optimization, and improvement of the accuracy of a functionnal using the adjoint state. In this work, we develop and analyze several strategies to evaluate the first- and second-derivatives of constrained functionals, using techniques based on Automatic Differentiation. Furthermore, we propose a descent algorithm for aerodynamic shape optimization, that is based on techniques of multi-level gradient, and which can be applied to different kinds of parameterization

On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics

International audienceThis article adresses the delicate issue of estimating physical uncertainties in aerodynamics. Usually, flow simulations are performed in a fully deterministic approach, although in real life operational uncertainty arises due to unpredictable factors that alter the flow conditions. In this article, we present and compare two methods to account for uncertainty in aerodynamic simulation. Firstly, automatic differentiation tools are used to estimate first- and second-order derivatives of aerodynamic coefficients with respect to uncertain variables, yielding an estimate of expectation and variance values (Method of Moments). Secondly, metamodelling techniques (radial basis functions, kriging) are employed in conjunction with Monte-Carlo simulations to derive statistical information. These methods are demonstrated for 3D Eulerian flows around the wing of a business aircraft at different regimes subject to uncertain Mach number and angle of attack

An exploratory fNIRS study with immersive virtual reality: a new method for technical implementation

For over two decades Virtual Reality (VR) has been used as a useful tool in several fields, from medical and psychological treatments, to industrial and military applications. Only in recent years researchers have begun to study the neural correlates that subtend VR experiences. Even if the functional Magnetic Resonance Imaging (fMRI) is the most common and used technique, it suffers several limitations and problems. Here we present a methodology that involves the use of a new and growing brain imaging technique, functional Near-infrared Spectroscopy (fNIRS), while participants experience immersive VR. In order to allow a proper fNIRS probe application, a custom-made VR helmet was created. To test the adapted helmet, a virtual version of the line bisection task was used. Participants could bisect the lines in a virtual peripersonal or extrapersonal space, through the manipulation of a Nintendo Wiimote ® controller in order for the participants to move a virtual laser pointer. Although no neural correlates of the dissociation between peripersonal and extrapersonal space were found, a significant hemodynamic activity with respect to the baseline was present in the right parietal and occipital areas. Both advantages and disadvantages of the presented methodology are discussed

Uncertainty Quantification for Robust Design

The objective of this chapter is to present, analyze and compare some practical methods that could be used in engineering to quantify uncertainty, for mechanical systems governed by partial differential equations. Most applications refer to aerodynamics, but the methods described in this chapter can be applied easily to other disciplines, such as structural mechanics

MATHICSE Technical Report : Isogeometric Analysis on V-reps: first results

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffuusion and linear elasticity

label free fluorescence detection of kinase activity using a gold nanoparticle based indicator displacement assay

A straightforward fluorescence indicator-displacement assay (IDA) has been developed for the quantitative analysis of ATP→ADP conversion

Secrecy Capacity and Secure Distance for Diffusion-Based Molecular Communication Systems

The biocompatibility and nanoscale features of Molecular Communication (MC) make this paradigm, based on molecules and chemical reactions, an enabler for communication theory applications in the healthcare at its biological level ( e.g. , bimolecular disease detection/monitoring and intelligent drug delivery). However, the adoption of MC-based innovative solutions into privacy and security-sensitive areas is opening new challenges for this research field. Despite fundamentals of information theory applied to MC have been established in the last decade, research work on security in MC systems is still limited. In contrast to previous literature focused on challenges, and potential roadmaps to secure MC, this paper presents the preliminary elements of a systematic approach to quantifying information security as it propagates through an MC link. In particular, a closed-form mathematical expression for the secrecy capacity of an MC system based on free molecule diffusion is provided. Numerical results highlight the dependence of the secrecy capacity on the average thermodynamic transmit power, the eavesdropper's distance, the transmitted signal bandwidth, and the receiver radius. In addition, the concept of secure distance in an MC system is introduced and investigated for two different techniques of signal detection, i.e. , based on energy and amplitude. The secrecy capacity can be used to determine how much secure information (bit/sec/Hz) can be exchanged and within which operative range, while the secure distance can be used to set the transmit power to obtain a secure channel at a given distance. We envision these metrics will be of utmost importance for a future design framework tailored to MC systems and their practical applications