Four Loop Result in SU(3)SU(3) Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the Langevin algorithm and the observables and to perform the expansion in \beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by one loop the previously known series.Comment: 9 pages. + 5 figures (postscript) appended at the end, (University of Parma, Dept.of Physics, report uprf-397-1994

CAUSTIQUES EN CHAMP PROCHE GENEREES PAR DES PARTICULES TRANSPARENTES RECONSTRUCTION PAR HOLOGRAPHIE NUMERIQUE EN LIGNE

International audienceL'holographie numerique en ligne est une technique d'imagerie volumetrique particulierement adaptee a la caracterisation spatiale (position, vitesse et tailles/morphologies) des ecoulements particulaires dilues. Dans de nombreux domaines la connaissance de la composition des particules est aussi d'un grand interet. Nous realisons cette mesure avec l'holographie numerique en ligne par l'analyse du champ proche des particules. Dans cette region les contributions des differents processus de diffusion de la lumiere peuvent etre plus facilement distinguees et notamment les caracteristiques du jet photonique (caustique vers l'avant generee par les rayons simplement refractes). La localisation dans l'espace du maximum d'intensite de cette caustique permet d'estimer l'indice de refraction relatif des particules. Dans cette communication, nous montrons que, dans le cadre de l'approximation de Fresnel de la diffraction scalaire, le jet photonique reconstruit par holographie numerique correspond a la tache d'Airy d'une lentille spherique. Par analogie avec les notions d'images virtuelles et reelles employees en optique pour les lentilles convergentes et divergentes, cette tache est restituee de facon reelle pour les particules ayant un indice relatif superieur a un et de facon virtuelle pour les particules dont l'indice relatif est plus petit que l'unite. Ceci fournit une solution simple et numeriquement tres efficace pour differencier ou caracteriser la composition des particules solides, liquides ou gazeuses. Une validation experimentale en laboratoire sur un ecoulement triphasique montre qu'il est desormais possible d'obtenir simultanement la position dans l'espace, la vitesse, la trajectoire, la taille et la composition de particules en ecoulement

CFD Ablation Predictions with Coupled GSI Modeling for Charring and non-Charring Materials

To this day, a major objective of TPS design is to reduce empiricism, and to increase fundamental modeling capability through increased understanding. One of the most challenging aspect is the proper coupling between the material response and the external flow field. With this regard, the goal of this research activity is the improvement of the numerical modeling capabilities through the development of advanced CFD tools integrated with Gas-Surface Interaction (GSI) modeling. Numerical prediction of ablation is ambitious and cpu-time demanding due to the complex multiphase physical and chemical processes that occur. With improvements in computational algorithms and advances in computer hardware, Navier- Stokes based approaches have become the norm in recent years for coupling to material thermal response predictions. The present state of the art in fluid-material coupling is represented by loose coupling of a high-fidelity CFD flow solver with a material thermal response code. In that respect, some major restrictions are still present in these state of the art coupled solutions: surface chemical equilibrium assumption non-ablating flow field prediction simplified diffusion modeling based on transfer coefficient Chemical equilibrium is a special condition of the general chemical nonequilibrium condition and surface recession rate predicted by the chemical equilibrium surface chemistry is usually reasonably conservative and is considered to be a best alternative when the nonequilibrium computation is too expensive or unlikely to be achieved. The ablation models are currently largely based on the surface equilibrium assumption and the effects and importance of non-equilibrium ablation models coupled with CFD tools are only beginning to be explored. Moreover, the coupling between CFD solver and material response code is often made considering non-ablating flow field solutions assuming a fully/super-catalytic, radiative equilibrium wall. This means that the effect on the flow field solution of the ablation and pyrolysis gas injection and of variable surface temperature are treated only approximately relying on the use of mass and energy transfer coefficients and semi-empirical blowing correction equations. Finally, the ablation rate is generally computed by the material response code using thermochemical tables and extremely simplified diffusion models based on transfer coefficients and semi-empirical relations relating mass and energy transfer. The objective of this research activity is to remove these major limiting assumptions developing suitable finite-rate GSI models and integrating CFD technology with Computational Surface Thermochemistry (CST) to take into account the effect of surface ablation and pyrolysis gas injection on the flow field and to allow surface ablation and surface temperature distributions to be determined as part of the CFD solution. Because the entire flow field is to be solved with ablative boundary conditions, the film-transfer theory assumption is no longer needed; this will permit to avoid all of the classical approximations such as transfer coefficients, equilibrium thermochemical tables, and blowing correction equations which needs to be used when ablative boundary conditions are not accounted for in the CFD solution. The ablative boundary conditions, based on finite-rate chemistry, species mass conservation and surface energy balance, is discretized and integrated with the CFD code to predict aerothermal heating, surface temperature, gas-phase surface composition, and surface ablation rate. The concentrations of chemical species at wall are determined from finite-rate gas-surface chemical reactions balanced by mass transfer rate. The surface temperature is determined from the surface energy balance assuming steady-state ablation or coupling with a thermal response code. The surface recession rate and the surface temperature are thus obtained as part of the flow field solution. The computational tool developed in this work is used to simulate two sets of experimental data for nozzle material ablation: sub-scale motor tests carried out for the Space Shuttle Reusable Solid Rocket Motor and the static firing tests of the second and third stage solid rocket motors of the European VEGA launcher which use carbon-carbon for the throat insert and carbon-phenolic for the region downstream of the throat

Understanding stochastic perturbation theory: toy models and statistical analysis

The numerical stochastic perturbation method based on Parisi-Wu quantisationis applied to a suite of simple models to test its validity at high orders.Large deviations from normal distribution for the basic estimators aresystematically found in all cases (``Pepe effect''). As a consequence oneshould be very careful in estimating statistical errors. We present someresults obtained on Weingarten's ``pathological'' model where reliable resultscan be obtained by an application of the bootstrap method. We also present someevidence that in the far less trivial application to Lattice Gauge Theory asimilar problem should not arise at moderately high loops (up toO(\alpha^{10}))

Kelvin-Helmholtz instability at proton scales with an exact kinetic equilibrium

The Kelvin-Helmholtz instability is a ubiquitous physical process in ordinary fluids and plasmas, frequently observed also in space environments. In this paper, kinetic effects at proton scales in the nonlinear and turbulent stage of the Kelvin-Helmholtz instability have been studied in magnetized collisionless plasmas by means of Hybrid Vlasov-Maxwell simulations. The main goal of this work is to point out the back reaction on particles triggered by the evolution of such instability, as energy reaches kinetic scales along the turbulent cascade. Interestingly, turbulence is inhibited when Kelvin-Helmholtz instability develops over an initial state which is not an exact equilibrium state. On the other hand, when an initial equilibrium condition is considered, energy can be efficiently transferred towards short scales, reaches the typical proton wavelengths and drives the dynamics of particles. As a consequence of the interaction of particles with the turbulent fluctuating fields, the proton velocity distribution deviates significantly from the local thermodynamic equilibrium, the degree of deviation increasing with the level of turbulence in the system and being located near regions of strong magnetic stresses. These numerical results support recent space observations from the Magnetospheric MultiScale mission of ion kinetic effects driven by the turbulent dynamics at the Earth's magnetosheath (Perri et al., 2020, JPlPh, 86, 905860108) and by the Kelvin-Helmholtz instability in the Earth's magnetosphere (Sorriso-Valvo et al., 2019, PhRvL, 122, 035102).Comment: 14 pages, 11 figure

Developments and new applications of numerical stochastic perturbation theory

A review of new developments in numerical stochastic perturbation theory (NSPT) is presented. In particular, the status of the extension of the method to gauge fixed lattice QCD is reviewed and a first application to compact (scalar) QED is presented. Lacking still a general proof of the convergence of the underlying stochastic processes, a self-consistent method for testing the results is discussed.Comment: 3 pages, 1 figure. Poster presented at the Lattice97 conference, Edinburgh, U

New issues for Numerical Stochastic Perturbation Theory

First attempts in the application of Numerical Stochastic Perturbation Theory (NSPT) to the problem of pushing one loop further the computation of SU(3) (SU(2)) pertubative beta function (in different schemes) are reviewed and the relevance of such a computation is discussed. Other issues include the proposal of a different strategy for gauge-fixed NSPT computations in lattice QCD.Comment: 3 pages, Latex, LATTICE98(algorithms

Power corrections and perturbative coupling from lattice gauge thoeries

From the analysis of the perturbative expansion of the lattice regularized gluon condensate, toghether with MC data, we present evidence of OPE-unexpected dim-2 power corrections in the scaling behaviour of the Wilson loop. These can be interpreted as an indication that in lattice gauge theories the running coupling at large momentum contains contributions of order Q^2.Comment: 3 pages, 2 figures. Talk given at the Lattice97 conference, Edinburgh, U

Effects of 5-year experimental warming in the Alpine belt on soil Archaea: Multi-omics approaches and prospects

We currently lack a predictive understanding of how soil archaeal communities may respond to climate change, particularly in Alpine areas where warming is far exceeding the global average. Here, we characterized the abundance, structure, and function of total (by metagenomics) and active soil archaea (by metatranscriptomics) after 5-year experimental field warming (+1°C) in Italian Alpine grasslands and snowbeds. Our multi-omics approach unveiled an increasing abundance of Archaea during warming in snowbeds, which was negatively correlated with the abundance of fungi (by qPCR) and micronutrients (Ca and Mg), but positively correlated with soil water content. In the snowbeds transcripts, warming resulted in the enrichment of abundances of transcription and nucleotide biosynthesis. Our study provides novel insights into possible changes in soil Archaea composition and function in the climate change scenario