Abstract
Implicit **particle**-**in**-**cell** **codes** offer advantages over their explicit counterparts **in** that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable for modeling the interaction of high-intensity laser pulses with overcritical plasmas, **in** the case where the electrostatic modes **in** the denser regions are of negligi- ble influence on the physical processes under study. To this goal, we have de- veloped the new two-dimensional electromagnetic code ELIXIRS (standing for ELectromagnetic Implicit X-dimensional Iterative Relativistic Solver) based on the relativistic extension of the so-called Direct Implicit Method [D. Hewett and A. B. Langdon, J. Comp. Phys. 72, 121(1987)]. Dissipation-free propagation of light waves into vacuum is achieved by an adjustable-damping electromagnetic solver. **In** the high-density case where the Debye length is not resolved, satisfac- tory energy conservation is ensured by the use of high-order weight factors. **In** this paper, we first present an original derivation of the electromagnetic direct implicit method within a Newton iterative scheme. Its linear properties are then investigated through numerically solving the relation dispersions obtained for both light and plasma waves, accounting for finite space and time steps. Finally, our code is successfully benchmarked against explicit **particle**-**in**-**cell** simulations for two kinds of physical problems: plasma expansion into vacuum and relativis- tic laser-plasma interaction. **In** both cases, we will demonstrate the robustness of the implicit solver for crude discretizations, as well as the gains **in** efficiency which can be realized over standard explicit simulations.

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D. PIC method, constraints, and accuracy
The PIC simulation is explicit (i.e., Poisson’s equation is solved at the beginning of each time step and charged par- ticles move during each time step assuming that the electric field does not change during that time step). This implies some strong constraints on the grid spacing dx and integra- tion time step dt, which must satisfy 24 dx < kDe and dt < 0:2=xpe where kDe and xpe are, respectively, the electron Debye length and angular plasma frequency. For the condi- tions above, with current densities below 400 A/m 2 we found that the Debye length was larger than 50 lm and the plasma frequency was on the order or less than 3 10 10 s 1 so we used a spatial grid of 500 200 and a time step on the order of 0.5 10 11 s. Accuracy and convergence of the results were tested and verified by using two different **Particle**-**In**- **Cell** simulation **codes** and varying the grid size and the num- ber of particles per **cell** (see Sec. V ). The PIC simulation code noted Code 1 **in** the following was used for similar sim- ulations presented **in** Ref. 19 and for simulations **in** other contexts. 25 – 28 The PIC simulation code indicated Code 2 was described and used **in** Refs. 29 and 30 . The two **codes** have been developed independently but are based on the same core principles of explicit **Particle**-**In**-**Cell** simulations. 31 One difference is that Code 1 uses digital filtering 31 of the space charge before solving Poisson’s equation, while Code 2 does not. Their implementation is slightly different since Code 1 is parallelized with the OpenMP (Open Multi- Processing) programming interface and operates on a 10 core processor, while Code 2 uses both OpenMP and MPI (Message Passing Interface) and operates on hundreds of cores.

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As the full system is rather complex, we will proceed step by step. First, we consider the SRS problem without spin, which was studied **in** several past works using a grid- based (Eulerian) Vlasov code (Huot et al. 2003; Ghizzo et al. 1990; Li et al. 2019b). As Eulerian **codes** are particularly stable and accurate over the entire phase space, we will use them as a benchmark for our PIC simulations. The benchmark will be carried out **in** the spin-less case, for which an Eulerian code is available. Second, we consider the spin Vlasov-Maxwell model studied **in** Sec. 2.2, but remove the effect of the plasma on the propagation of the electromagnetic wave. This amounts to assuming that the wave propagates freely (as **in** vacuum) and interacts with the plasma, but the plasma does not impact the propagation of the wave. **In** contrast, the longitudinal nonlinearity due to Poisson’s equation is maintained. **In** this case, an approximate solution of the spin dynamics can be obtained analytically, which enables us to validate the numerical simulations. Finally, we simulate the complete spin-dependent model (2.7) and study the influence of the various physical parameters: amplitude of the electromagnetic wave, temperature, initial electron polarization, and scaled Planck constant.

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Keywords: **particle**-**in**-**cell**, parallel implementation, wall interaction, neutral dynamics, differential cross-section
1. INTRODUCTION
Low-pressure gas discharges and plasma sources are used **in** a great variety of applications [ 1 , 2 ], such as space propulsion [ 3 , 4 ], neutral beam injection [ 5 ] and plasma separation [ 6 – 8 ]. To optimize these devices and expand the range of application of low-pressure plasmas, numerical modeling capabilities are highly desirable. Yet, experimental results indicate that such plasmas are often far from thermal equilibrium [ 2 ]. Furthermore, the mean free path of charge particles **in** low-pressure discharges is often comparable to, if not greater than, the vacuum vessel dimensions. Under such conditions standard fluid models do not hold [ 9 , 10 ] and fluid simulation tools can not fully capture the physics at play. **In** these plasma regimes, kinetic modeling tools such as **particle**-**in**-**cell** (PIC) techniques [ 11 – 13 ] and Vlasov’s **codes** [ 14 , 15 ] are required for high-fidelity simulations. Kinetic modeling however comes at a significantly larger computing cost which sets an upper limit to the plasma density and plasma volume one can model. This **in** turn limits the applicability of PIC techniques for whole device simulations. Yet, owing to the expansion of parallel computing, PIC techniques are increasingly used to model a large range of low-pressure plasma sources [ 16 – 19 ].

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Pressure sensors are placed at different heights on the tube, from which the local pressure drop of the suspension can be measured and thus the suspension void fraction is calculated.
**In** operation, the DiFB is ﬂuidised at a gas velocity U f slightly higher than the minimum bubbling velocity. Pressurising the DiFB bed induces the solids to rise **in** the tube, transforming the system into an Upﬂow Bubbling Fluid Bed (UBFB). The operating para- meters are the ﬂuidisation ﬂow rate of the dispenser ﬂuidised bed (Q f ), the aeration ﬂow rate **in** the tube (Q ae ) and the relative pressure of the DiFB freeboard (P fb ). Helium gas tracer was injected **in** the different gas injection points and the helium concentration was measured at the top of the bed as a function of time with a micro-volume thermal conductivity detector. Only 5% of the gas injected at the bottom of the ﬂuidised bed travels up the transport tube since 95% is released through the pressure regulator valve. The helium tracing of the gas phase demonstrated that the gas ﬂow **in** the transport tube is only upward.

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Dense gas–solid suspensions have the potential to be applied as heat transfer ﬂuids (HTF) for energy collection and storage **in** concentrated solar power plants. At the heart of these systems is the solar receiver, composed of a bundle of tubes which contain the solid suspension used as the thermal energy carrier. **In** the design investigated here, the particles form a dense upward-ﬂowing suspension. Both density of the suspension of these particles and their movement have a strong inﬂuence on the heat transfer. An apparatus was designed to replicate the hydrodynamic and **particle** motion **in** the real solar energy plant at ambient temperature. The governing parameters of the ﬂow were established as the solid feeding ﬂow rate, the ﬂuidisation velocity, the solids holdup, the freeboard pressure and the secondary air injection (aeration) velocity. **In** the case studied, aeration was applied with air introduced into the uplift transport tube some way up its length. This study ﬁnds that the amount of this secondary air injection is the most important parameter for the stability and the uniform distribution of the solids ﬂow **in** the tubes. Solids motion was measured using the non-invasive positron emission **particle** tracking (PEPT) technique to follow the movement of a 60 mm tracer **particle**, onto which was adsorbed the

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3 MultiScale Material Science for Energy and Environment, UMI 3466 CNRS-MIT, CEE, Massachusetts Institute of Technology,
77 Massachusetts Avenue, Cambridge 02139, USA (Received 27 August 2014; published 9 February 2015)
**Particle** degradation and fracture play an important role **in** natural granular flows and **in** many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing **cell** shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on **cell** shape distribution. We show that this distribution may be understood **in** terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to **particle** size dependence of the compressive strength **in** good agreement with our simulation data.

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VII. CONCLUSION
We studied the feasibility to produce and extract a hy- drogen negative ion current (generated inside the plasma volume of a linear device through collisions between charged particles and the background gas) with a magni- tude relevant to the requirements of magnetic fusion ma- chine’s Neutral Beam Injectors (NBI). Linear devices are interesting configurations as the electrons are strongly magnetised with field lines aligned with the discharge axis. The large aspect ratio of the discharge (defined as the axial length over the cylinder radius) implies that electrons will oscillate between the end-plates located at the extremities of the cylinder and diffuse slowly across the magnetic field. Negative ions are produced inside the plasma **in** a two step process consisting of (i) a region with an electron temperature between 5 and 10 eV where the hydrogen background gas is excited vibrationally. (ii) a second area, with a temperature below 1 eV where the negative ions are generated as a byproduct of the dis- sociative attachment of a hydrogen molecule due to a collision with an electron. The residence time of the lat- ter inside the ion source hence has an incidence on the production yield of the negative ions. We showed that biasing negatively the end-plates does increase the elec- tron residence time by an order of magnitude and as a consequence the negative ion density may be increased by a factor ∼ 3 for a given absorbed RF power. Bias- ing the end-plates induce a reduction of the amplitude of the plasma potential which is a limiting factor for the negative ion density as the potential profile switches to a well when the end-plate voltage is such that one collects a higher ratio of positive ions compared to electrons. **In** that case, the plasma potential extract radially the nega- tive ions. One observes that the negative ion density has a ring-like shape with a maximum at the location where

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the help of a computer, will certainly yield **codes** with smaller density. We made no attempt to optimize the second phase **in** the lower bound proof. Doing more complicated discharging rules, based on more complicated properties of identifying **codes** will surely give better bounds. However, we do not see any way to make the two bounds meet for all k. Nevertheless, we are able to do it for k = 3 : we show that d ∗ (S

Other possible extensions may be considered and will be the subject of future works. First, it would be interesting to deal with Dirichlet boundary conditions (**in**- stead of periodic ones) for enlarging the application field. For the same reason, more general collision operators should be considered, combining this approach with re- laxation techniques as **in** [12]. Extension to higher dimensions of the phase-space is also possible and a comparison with semi-Lagrangian schemes would be interesting. Acknowledgements. A. Crestetto would like to thank the ANR Project GEONUM (ANR-12-IS01-0004-01), N. Crouseilles the ERC Starting Grant Project GEOP- ARDI and M. Lemou the ANR Project LODIQUAS (ANR-11-IS01-0003) for their financial supports.

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Pour pallier ` a ces d´esagr´ements, les chercheurs et les ing´enieurs ont d´evelopp´e de nombreux **codes** permettant de d´etecter ou mˆeme de corriger certaines erreurs. Dans une conversation normale entre deux personnes, lorsqu’un des interlocuteurs ne comprend pas un message, il demande en g´en´eral qu’on lui r´ep`ete une phrase ou un mot. Ainsi, pour ˆetre compris par un plus grand nombre, un discours est souvent plus long que n´ecessaire. Les id´ees principales sont reprises et r´ep´et´ees. On ajoute donc une certaine redondance par rapport au message initial.

60 "QD446 " "disease mongering "
Melissa's comments: **In** your paper "The words of prevention, part II: ten terms **in** the realm of quaternary prevention," you noted that there are no MeSH terms for "disease mongering." I also checked for other terms and did not find any appropriate terms. I even searched PubMed for "disease mongering" and reviewed the articles for MeSH terms.

ise of that theorem was great: a probability of error exponentially small in the block length at any information rate below channel capacity.. Finding a way of im[r]

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The Kaggle Higgs Boson challenge (**in** HEP terms)
• Data comes as a finite set
D = {(x i , y i , w i )|i = 0, . . . , N − 1}, where x i ∈ R d , y i ∈ {signal, background} and w i ∈ R + . • The goal is to find a region G = {x| g (x) = signal } ⊂ R d ,

We strongly believe that both our upper and lower bounds may be improved using the same general techniques. **In** fact, to obtain the upper bound, we only alter the code C G ∗ on the top two rows and the bottom two rows of S k . Looking
for alterations on more rows, possibly with the help of a computer, will cer- tainly yield **codes** with smaller density. We made no attempt to optimize the second phase **in** the lower bound proof. Doing more complicated discharging rules, based on more complicated properties of identifying **codes** will surely give better bounds. However, we do not see any way to make the two bounds meet for all k. Nevertheless, we are able to do it for k = 3 : we show that d ∗ (S 3 ) = 18 7 .

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αβ . (3.15)
Navier-Stokes hydro has the drawback of being acausal [117, 118]. Short wave length perturbation modes, outside of the validity range of the gradient expansion **in** any case, grow exponentially due to superluminal signal propagation. This leads to physical and numerical instabilities, as explained e.g. **in** [110]. Any numerical implementation of relativistic viscous hydrodynamics must thus include second or- der terms **in** the gradient expansion. The most widely used such frameworks are the Israel-Stewart theory [119, 120] and the BRSSS theory [121]. **In** BRSSS hydro- dynamics, the expression found for the stress tensor is computed using conformal symmetry, and it can be found to depend upon the curvature of the manifold consid- ered. Since we will work **in** the framework of Navier-Stokes hydrodynamics, we will not go into more detail here. Working at this first-order level is acceptable because we only consider a finite number of hydrodynamic modes, **in** which case the issue of causality is less significant.

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Polarisation des **codes** Note technique (Polar **Codes**, extrait des travaux de l’EPFL)
JP Cances, Xlim, UMR 7252
Cette note technique a pour objet de montrer comment l’algorithme de décodage itératif s’applique sur les **codes** polaires et elle s’inspire des travaux de R Urbank à l’EPFL.

Contexte et rappel de quelques notions sur la physique des plasmas 17
le déplacement des particules chargées.
Dans la littérature, il existe différents types d’approximation numérique de l’équation de Vlasov, couplée non linéairement aux équations de Maxwell. Les mé- thodes utilisées sont les méthodes particulaires, les méthodes spectrales basées sur des développements de Fourier [Klimas et Farrell (1987), Klimas et Farrell (1994)] et parfois de Hermite [Holloway (1996)] de la fonction de distribution et les mé- thodes utilisant un maillage de l’espace des phases. Dans les méthodes particulaires, nous avons la méthode **Particle**-**In**-**Cell** (PIC), appelée aussi méthode lagrangienne [Birdsall et Langdon (1991), Hockney et Eastwood (1988)] et la méthode de type Smooth **Particle** Hydrodynamics (SPH) [Bateson et Hewett (1998)]. La méthode PIC date des années 1950 [Dawson (1962), Buneman (1959)] et a été formalisée dans les années 1970. Cette méthode, très utilisée, consiste à remplacer l’équation de Vlasov par les équations de mouvement. Une variante de la méthode PIC, appelée méthode δf, est aussi utilisée, en particulier quand la physique étudiée est proche d’un état d’équilibre. Le principe de cette méthode est de développer la fonction de distribution au voisinage d’un équilibre connu (f 0 ) en f = f 0 + δf et d’approximer uniquement la partie δf par une méthode PIC. La méthode SPH consiste, quant à elle, à considérer un nombre limité de particules de forme gaussienne dont les caractéristiques peuvent varier et qui interagissent les unes avec les autres. Une autre méthode particulaire, similaire à la méthode SPH, a été introduite par Bateson et Hewett [Bateson et Hewett (1998)], dans laquelle ils font évoluer un nombre relati- vement faible de macro-particules de forme gaussienne. Dans la méthode spectrale, appelée aussi méthode splitting d’opérateurs, l’équation de Vlasov se décompose en deux parties, en raison de la présence de deux champs d’advection indépendants

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is related to φ(x) via a Legendre transform [44, 45].
**In** the present work we apply the macroscopic fluctuation theory (MFT) to single-file diffusion. The MFT was developed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim [46–50] for calculating large deviation functions **in** classical diffusive systems; similar results were obtained **in** the context of shot noise **in** conductors [51, 52]. The MFT provides a significant step towards constructing a general theoretical framework for non-equilibrium systems [44, 53]. Over the past decade the MFT has been successfully applied to numerous systems [46–48, 53–70]. A perfect agreement between the MFT and microscopic calculations has been observed whenever results from both approaches were available. The MFT is a powerful and versatile tool, although the analysis is involved and challenging **in** most cases. The MFT allows one to probe large deviations of macroscopic quantities such as the total current. Intriguingly, large deviations of an individual microscopic **particle** **in** a single-file system can be captured by the MFT [29, 69]. The essential property of single-file systems—the fixed order of the particles— allows us to express the displacement of the tagged **particle** **in** a way amenable to the MFT treatment. The MFT is an outgrowth of fluctuating hydrodynamic [71]. Using a path integral formulation one associates a classical action to a particular time evolution of the system. The optimal path has the least action and the analysis boils down to solving the Hamilton equations corresponding to the least-action paths. The advantage is that within this formulation all the microscopic details of the

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