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Publication# On the coupling between an ideal fluid and immersed particles

Résumé

In this paper, we present finite-dimensional particle-based models for fluids which respect a number of geometric properties of the Euler equations of motion. Specifically, we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. We substitute the use of principal connections in Cendra et al. (2001) [13] with vector field valued interpolations from particle velocity data. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it provides estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle spectral methods, where the error analysis is "built in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help us achieve a particle-centric version of Kelvin's circulation theorem. (C) 2013 Elsevier B.V. All rights reserved.

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Francesco Cerutti, Nikolaos Charitonidis, André Donadon Servelle, Philippe Jean Schoofs

FLUKA is a general purpose Monte Carlo code able to describe the transport and interaction of any particle and nucleus type in complex geometries over an energy range extending from thermal neutrons to ultrarelativistic hadron collisions. It has many different applications in accelerator design, detector studies, dosimetry, radiation protection, medical physics, and space research. In 2019, CERN and INFN, as FLUKA copyright holders, together decided to end their formal collaboration framework, allowing them henceforth to pursue different pathways aimed at meeting the evolving requirements of the FLUKA user community, and at ensuring the long term sustainability of the code. To this end, CERN set up the FLUKA.CERN Collaboration (1) . This paper illustrates the physics processes that have been newly released or are currently implemented in the code distributed by the FLUKA.CERN Collaboration (2) under new licensing conditions that are meant to further facilitate access to the code, as well as intercomparisons. The description of coherent effects experienced by high energy hadron beams in crystal devices, relevant to promising beam manipulation techniques, and the charged particle tracking in vacuum regions subject to an electric field, overcoming a former lack, have already been made available to the users. Other features, namely the different kinds of low energy deuteron interactions as well as the synchrotron radiation emission in the course of charged particle transport in vacuum regions subject to magnetic fields, are currently undergoing systematic testing and benchmarking prior to release. FLUKA is widely used to evaluate radiobiological effects, with the powerful support of the Flair graphical interface, whose new generation (Available at http://flair.cem) offers now additional capabilities, e.g., advanced 3D visualization with photorealistic rendering and support for industry-standard volume visualization of medical phantoms. FLUKA has also been playing an extensive role in the characterization of radiation environments in which electronics operate. In parallel, it has been used to evaluate the response of electronics to a variety of conditions not included in radiation testing guidelines and standards for space and accelerators, and not accessible through conventional ground level testing. Instructive results have been obtained from Single Event Effects (SEE) simulations and benchmarks, when possible, for various radiation types and energies. The code has reached a high level of maturity, from which the FLUKA.CERN Collaboration is planning a substantial evolution of its present architecture. Moving towards a modern programming language allows to overcome fundamental constraints that limited development options. Our long term goal, in addition to improving and extending its physics performances with even more rigorous scientific oversight, is to modernize its structure to integrate independent contributions more easily and to formalize quality assurance through state-of-the-art software deployment techniques. This includes a continuous integration pipeline to automatically validate the codebase as well as automatic processing and analysis of a tailored physics-case test suite. With regard to the aforementioned objectives, several paths are currently envisaged, like finding synergies with Geant4, both at the core structure and interface level, this way offering the user the possibility to run with the same input different Monte Carlo codes and crosscheck the results.

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

László Forró, Richard Gaal, Sylvia Jeney, Flavio Maurizio Mor

Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibration method. A well-known calibration procedure is to record the stochastic motion of the trapped particle and compare its statistical behavior with the theory of the Brownian motion in a harmonic potential. Here we present an interactive calibration software which allows for the simultaneous fitting of three different statistical observables (power spectral density, mean square displacement and velocity autocorrelation function) calculated from the trajectory of the probe to enhance fitting accuracy. The fitted theory involves the hydrodynamic interactions experimentally observable at high sampling rates. Furthermore, a qualitative extension is included in our model to handle the thermal fluctuations in the orientation of optically trapped asymmetric objects. The presented calibration methodology requires no prior knowledge of the bead size and can be applied to non-spherical probes as well. The software was validated on synthetic and experimental data. Program summary Program title: PFMCal Catalogue identifier: AEXH_v1_0 Program summary URL: http://cpc.cs.qub.ac.ukisummaries/AEXH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 206,399 No. of bytes in distributed program, including test data, etc.: 10,319,465 Distribution format: tar.gz Programming language: MatLab 2011a (Math Works Inc.). Computer: General computer running MatLab (MathWorks Inc.), using Statistics Toolbox. Operating system: Any which supports Matlab using Statistics Toolbox. RAM: 10 MB Classification: 3, 4.9, 18, 23. Nature of problem: Calibration of optical tweezers by measuring the Brownian motion of the trapped object. The voltage-to-displacement ratio of the detection system (the inverse of the sensitivity), the stiffness of the trap and the size of the bead are obtained via the simultaneous fitting of the power spectral density (PSD), mean square displacement (MSD) and velocity autocorrelation (VAF) functions calculated from the trajectory. The calibration can be performed for non-spherical probes as well. Solution method: Initialization points for all parameters are inferred from characteristic features of the statistical observables (PSD, MSD and VAF) based on the method developed by Grimm et al. in [1]. Theoretical functions for the PSD, the MSD and the VAF are calculated from the model of Brownian motion confined by a harmonic potential taking hydrodynamic interactions into consideration [2-4]. This calibration methodology has been successfully used in actual experiments with micro-spheres [5, 6]. Calculated functions are fitted to the measurement data via the Levenberg-Marquardt least square fitting routine available in the MatLab Optimalization Toolbox, using the nlinfit function. If the error to the measured data has been estimated, the corresponding data values can be weighted by the inverse of the standard error squared in order to eliminate bias introduced by heteroscedasticity. In order to increase robustness and avoid convergence to local minima, minimum search from multiple initial values in the vicinity of the first guess is possible. Additional comments: Input of the program is the experimental PSDexp, MSDexp, and VAF(exp) data points calculated from the measured x, y and z projections of the trajectory of the particle. The data may best be blocked and may optionally contain an error for each data point for better results. The data should be formatted into three columns: 1. independent variables (time or frequency array), 2. function values, 3. optionally, error values (e.g. standard error calculated from the binning) to improve fitting efficiency. In case error values were not estimated, the third column should be filled with zeros. The first row is reserved for a header, data is read from the second row. Data size should not be larger than a few hundreds of rows, otherwise, using larger blocks for binning is advised. In order to observe the short time behavior of the Brownian motion, influenced by hydrodynamic effects, the sampling rate should be typically higher than 100 kHz. Total sampling time is typically tens of seconds, to achieve a good resolution in the frequency range. The optical axis of the laser, the microscope and the detector system should be co-aligned to exclude artificial crosstalk between the x, y and z channels of the position detector. Running time: Seconds (C) 2015 Elsevier B.V. All rights reserved.