Non-linear effects and shock formation in the focusing of a spherical acoustic wave : Numerical simulations and experiments in liquid helium

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, non-linear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of non-linearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. The comparison between numerical and experimental results allows in particular to calibrate the vibration of the ceramics used to produce the wave, as a function of the applied voltage.Comment: 20 pages, 26 figures. Submitted to The European Physical Journal

Model and system learners, optimal process constructors and kinetic theory-based goal-oriented design: a new paradigm in materials and processes informatics

Traditionally, Simulation-Based Engineering Sciences (SBES) has relied on the use of static data inputs (model parameters, initial or boundary conditions, ... obtained from adequate experiments) to perform simulations. A new paradigm in the field of Applied Sciences and Engineering has emerged in the last decade. Dynamic Data-Driven Application Systems [9, 10, 11, 12, 22] allow the linkage of simulation tools with measurement devices for real-time control of simulations and applications, entailing the ability to dynamically incorporate additional data into an executing application, and in reverse, the ability of an application to dynamically steer the measurement process. It is in that context that traditional "digital-twins" are giving raise to a new generation of goal-oriented data-driven application systems, also known as "hybrid-twins", embracing models based on physics and models exclusively based on data adequately collected and assimilated for filling the gap between usual model predictions and measurements. Within this framework new methodologies based on model learners, machine learning and kinetic goal-oriented design are defining a new paradigm in materials, processes and systems engineering

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring a prominence never imagined. In the past, in the domain of materials, processes and structures, testing machines allowed extract data that served in turn to calibrate state-of-the-art models. Some calibration procedures were even integrated within these testing machines. Thus, once the model had been calibrated, computer simulation takes place. However, data can offer much more than a simple state-of-the-art model calibration, and not only from its simple statistical analysis, but from the modeling and simulation viewpoints. This gives rise to the the family of so-called twins: the virtual, the digital and the hybrid twins. Moreover, as discussed in the present paper, not only data serve to enrich physically-based models. These could allow us to perform a tremendous leap forward, by replacing big-data-based habits by the incipient smart-data paradigm

Knot undulator to generate linearly polarized photons with low on-axis power density

Heat load on beamline optics is a serious problem to generate pure linearly polarized photons in the third generation synchrotron radiation facilities. For permanent magnet undulators, this problem can be overcome by a figure-8 operating mode. But there is still no good method to tackle this problem for electromagnetic elliptical undulators. Here, a novel operating mode is suggested, which can generate pure linearly polarized photons with very low on-axis heat load. Also the available minimum photon energy of linearly polarized photons can be extended much by this method

Hybrid constitutive modeling: data-driven learning of corrections to plasticity models

In recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing models, and present deviations from the most popular ones, we believe that this does not justify (or, at least, not always) to abandon completely all the acquired knowledge on the constitutive characterization of materials. Instead, what we propose here is, by means of machine learning techniques, to develop correction to those popular models so as to minimize the errors in constitutive modeling

Data-Driven Computational Plasticity

The use of constitutive equations calibrated from data collected from adequate testing has been implemented successfully into standard solvers for successfully addressing a variety of problems encountered in SBES (simulation based engineering sciences). However, the complexity remains constantly increasing due to the more and more fine models being considered as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy.), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Data-driven simulation consists of directly linking data to computers in order to perform numerical simulations. These simulations will use universal laws while minimizing the need of explicit, often phenomenological, models. This work revisits our former work on data-driven computational linear and nonlinear elasticity and the rationale is extended for addressing computational inelasticity (viscoelastoplasticity)

A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, ...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be confident on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority of existing models lack of generality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. This technique is based on the use of manifold learning methodologies, that allow to extract the relevant information from large experimental datasets

A manifold learning approach for integrated computational materials engineering

Image-based simulation is becoming an appealing technique to homogenize properties of real microstructures of heterogeneous materials. However fast computation techniques are needed to take decisions in a limited time-scale. Techniques based on standard computational homogenization are seriously compromised by the real-time constraint. The combination of model reduction techniques and high performance computing contribute to alleviate such a constraint but the amount of computation remains excessive in many cases. In this paper we consider an alternative route that makes use of techniques traditionally considered for machine learning purposes in order to extract the manifold in which data and fields can be interpolated accurately and in real-time and with minimum amount of online computation. Locallly Linear Embedding is considered in this work for the real-time thermal homogenization of heterogeneous microstructures

The energy budget in Rayleigh-Benard convection

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of Ra^{0.5}. The scaling of the mean square velocity is closer to Ra^{0.46}, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.Comment: 5 pages, 3 figures, new version 13 Mar, 200