Controlling the generation of high frequency electromagnetic pulses with relativistic flying mirrors using an inhomogeneous plasma

A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties.     

Pierre Turq,an inspirational scientist in charge and at interfaces

Pierre Turq has made decisive contributions to the theory and to the multiscale simulation of charged systems, such as molten salts, electrolyte solutions and colloidal suspensions, in the bulk, at interfaces and under confinement. His research line focussed on dynamical properties and was characterised by constant efforts to connect his theoretical work to both experiments and practical applications. In this article, his colleagues and former students pay a tribute to his past and current research interests by illustrating some recent developments accomplished in his laboratory.     

Dual-mode registration of dynamic contrast-enhanced ultrasound combining tissue and contrast sequences

This study proposes a new method for automatic, iterative image registration in the context of dynamic contrast-enhanced ultrasound (DCE-US) imaging. By constructing a cost function of image registration using a combination of the tissue and contrast-microbubble responses, this new method, referred to as dual-mode registration, performs alignment based on both tissue and vascular structures. Data from five focal liver lesions (FLLs) were used for the evaluation. Automatic registration based on the dual-mode registration technique and tissue-mode registration obtained using the linear response image sequence alone were compared to manual alignment of the sequence by an expert. Comparison of the maximum distance between the transformations applied by the automatic registration techniques and those from expert manual registration reference showed that the dual-mode registration provided better precision than the tissue-mode registration for all cases. The reduction of maximum distance ranged from 0.25 to 9.3 mm. Dual-mode registration is also significantly better than tissue-mode registration for the five sequences with p  -values lower than 0.03$0.03$. The improved sequence alignment is also demonstrated visually by comparison of images from the sequences and the video playbacks of the motion-corrected sequences. This new registration technique better maintains a selected region of interest (ROI) within a fixed position of the image plane throughout the DCE-US sequence. This should reduce motion-related variability of the echo-power estimations and, thus, contribute to more robust perfusion quantification with DCE-US.     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s

In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces.     

Optical sectioning in wide-field microscopy obtained by dynamic structured light illumination and detection based on a smart pixel detector array

Optical sectioning in wide-field microscopy is achieved by illumination of the object with a continuously moving single-spatial-frequency pattern and detecting the image with a smart pixel detector array. This detector performs an on-chip electronic signal processing that extracts the optically sectioned image. The optically sectioned image is directly observed in real time without any additional postprocessing.     

Second-order hyperbolic s.p.d.e.'s driven by homogeneous Gaussian noise on a hyperplane

We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.

     

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L ¹ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula α_phys ≃ α(1 + 2α/(3π) log Λ)⁻¹, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is  ≤  2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.