In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms. Unitary representations of this group describe a wide variety of quantum systems, and have predicted previously unsuspected possibilities; notably, anyons and nonabelian anyons in two space dimensions. We present here foundational reasons why this semidirect product group serves as a universal kinematical group for quantum mechanics. We obtain thus a unified account of all possible quantum kinematics for systems with mass in an arbitrary physical space, and clarify the role played by topology in quantum mechanics. Our development does not require quantization of classical phase space; rather, the classical limit follows from the quantum mechanics. We also consider the relationship of our development to Heisenberg quantization.

The alphas (αb, αs) and thetas (θb, θs) are the essential parameters describing the asymptotic growth behavior of the mixing layer driven by Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the interface between the fluids. Extensive simulations and experiments have been conducted in the determination of these parameters. The results depend on numerical algorithms, resolutions, and the accuracy of experimental measurements. In this article, we present a unique relationship between the alphas and thetas by applying a simple buoyancy-drag mixing model. Our first main result is that, for the same fluids, these parameters are not independent because they are fundamentally connected by physics principles and they all are functions of the drag coefficients of the fluids. As a consequence, the alphas and thetas are intrinsically coupled. All are functions of any single one of these. Our second main result is that the RT bubble growth rate (αb) is determined by the bubble competition process – a merger model – at the edge of the mixing layer. Together, these two main results determine all the alphas and thetas by strictly theoretical reasoning. Applications to both hydro and laser driven experiments at OMEGA are presented.

The alphas (alpha(b), alpha(s)) and thetas (theta(b), theta(s)) are the essential parameters describing the asymptotic growth behavior of the mixing layer driven by Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities at the interface between the fluids. Extensive simulations and experiments have been conducted in the determination of these parameters. The results depend on numerical algorithms, resolutions, and the accuracy of experimental measurements. In this article, we present a unique relationship between the alphas and thetas by applying a simple buoyancy-drag mixing model. Our first main result is that, for the same fluids, these parameters are not independent because they are fundamentally connected by physics principles and they all are functions of the drag coefficients of the fluids. As a consequence, the alphas and thetas are intrinsically coupled. All are functions of any single one of these. Our second main result is that the RT bubble growth rate (alpha(b)) is determined by the bubble competition process - a merger model - at the edge of the mixing layer. Together, these two main results determine all the alphas and thetas by strictly theoretical reasoning. Applications to both hydro and laser driven experiments at OMEGA are presented. (C) 2020 Elsevier B.V. All rights reserved.

Three algorithms have been proposed for solution of the Rayleigh–Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow. The principles serve to select the physically relevant solution from among many nonunique solutions. The admissibility principle is in dispute. The three different algorithms, expressing the three physical admissibility principles can be formulated in terms of the three energy dissipation rates or the entropy production rates, as selected by the size of the sub grid scale coefficients. These have maximal values or less than maximal values. The resulting solutions are markedly different.We find strong validation evidence that supports the maximum rate principle, based on a review of prior results and on new results presented here. We review experimental data used for validation and sufficient to discriminate among the three. We present a new analysis of this data. We show that the hypothesized long wave length perturbations in the initial conditions are not significant, so that validation can be based on this data in a straight forward manner.One of the algorithms is labeled direct numerical simulation, but is not, and as a consequence, the two algorithms with less than maximal SGS coefficients are variants of one another.Recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed.

Diffeomorphism groups and their unitary representations unify the description of a wide variety of diverse nonrelativistic (Galilean) quantum systems. In recent work, we have suggested an approach to relativistic quantum field theory that begins with hierarchies of diffeomorphism group representations and the corresponding current densities. We introduce (noncovariant) creation and annihilation fields that intertwine the representations, and restore the (relativistic) spacetime symmetry by redefining local quantum fields and the Hamiltonian operator in terms of the intertwining fields and current densities. Here we outline the main ideas, and point to next steps and possible future directions of this line of inquiry.

Three very different algorithms have been proposed for solution of the Rayleigh-Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow, which serve to complete these underspecified equations by selection of the physically relevant solution from among the many otherwise nonunique solutions of these equations. The disputed physical principle is the admissibility condition which selects the physically meaningful solution from among the myriad of nonphysical solutions. The three different algorithms, expressing the three physical admissibility principles, are formulated alternately in terms of the energy dissipation rate or the entropy production rate. The three alternatives are zero, minimal or maximal rates. The solutions are markedly different. We find strong validation evidence that supports the solution with the maximum rate of dissipated energy, based on a review of prior results and new results presented here. Our verification reasoning, consisting of mathematical analysis based on physics assumptions, also supports the maximum energy dissipation rate and reasons against the other two. The zero dissipation solution is based on claims of direct numerical simulation. We dispute these claims and introduce analysis indicating that such simulations are far from direct numerical simulations. Recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed.

We present two main results. The first is a plausible validation argument for the principle of a maximal rate of entropy production for Euler equation turbulence. This principle can be seen as an extension of the second law of thermodynamics. In our second main result, we examine competing models for large eddy simulations of Euler equation (fully developed) turbulence. We compare schemes with no subgrid modeling, implicit large eddy simulation (ILES) with limited subgrid modeling and those using dynamic subgrid scale models. Our analysis is based upon three fundamental physical principles: conservation of energy, the maximum entropy production rate and the principle of universality for multifractal clustering of intermittency. We draw the conclusion that the absence of subgrid modeling, or its partial inclusion in ILES solution violates the maximum entropy dissipation rate admissibility criteria. We identify circumstances in which the resulting errors have a minor effect on specific observable quantities and situations where the effect is major. Application to numerical modeling of the deflagration to detonation transition in type Ia supernova is discussed.

In this paper a simple model is proposed in which the observed φ and ω resonant states are considered as mixtures of "pure" states |Y〉 and |B〉 corresponding to hypercharge and baryonic mesons. The implications of this model for the isoscalar nucleon form factor; the decays of the φ, ω, and π0 mesons; the role of the ω and φ mesons in nuclear forces; the mass distribution of Dalitz pairs in the decay π0→γ+e++e-; and the photoproduction of η mesons are briefly considered.

The “holy-grail” of renewable energy — nuclear fusion — has long been sought for its clean and effectively endless potential for energy generation. One of the most studied means of achieving fusion, is inertial confinement fusion (ICF), which has been the focus of much study for the past 50 years. The fundamental goal of ICF is to compress and heat a fuel source (often solid Deuterium-Tritium, DT) into the smallest volume possible. In addition to the pertinent multi-component, and multi-phase physics dictating the implosion dynamics, a trove of hydrodynamic instabilities are known to be active throughout the implosion. These include the Rayleigh-Taylor instability on the surface of the accelerating capsule, Richtmyer-Meshkov instability due to interactions with the generated strong shocks, and general asymmetries of the fuel capsule which are amplified during the implosion. A full understanding of how these instabilities manifest in ICF is necessary in order to effectively mitigate their growth and permit a sustained thermonuclear burn. These classical instabilities have been the topic of much study in the past few decades, but in addition to these instabilities which amplify asymmetries seeded by manufacturing the target or by the impulse itself, it has recently been shown that the presence of a fill tube, which is employed to replenish fuel, is able to seed a large-scale perturbation, as suggested by the numerical simulation results in Ref. [1]. Those simulations identified the shadowing of radiation due to the ablated SiO2 fill-tube material as a potential perturbation influencing the implosion. It was also noticed that a radially impinging jet was generated as the fill tube is crushed and remaining DT fuel is squeezed out. Nonetheless, the results did not indicate the same degradation in yield as

In large eddy simulations, the Reynolds averages of nonlinear terms are not directly computable in terms of the resolved variables and require a closure hypothesis or model, known as a subgrid scale term. Inspired by the renormalization group (RNG),we introduce an expansion for the unclosed terms, carried out explicitly to all orders. In leading order, this expansion defines subgrid scale unclosed terms, which we relate to the dynamic subgrid scale closure models. The expansion, which generalizes the Leonard stress for closure analysis, suggests a systematic higher order determination of the model coefficients. The RNG point of view sheds light on the nonuniqueness of the infinite Reynolds number limit. For the mixing of N species, we see an N+1 parameter family of infinite Reynolds number solutions labeled by dimensionless parameters of the limiting Euler equations, in a manner intrinsic to the RNG itself. Large eddy simulations, with their Leonard stress and dynamic subgrid models, break this nonuniqueness and predict unique model coefficients on the basis of theory. In this sense large eddy simulations go beyond the RNG methodology, which does not in general predict model coefficients.

We review existence and non-uniqueness results for the Euler equation of fluid flow. These results are placed in the context of physical models and their solutions. Non-uniqueness is in direct conflict with the purpose of practical simulations, so that a mitigating strategy, outlined here, is important. We illustrate these issues in an examination of mesh converged turbulent statistics, with comparison to laboratory experiments.

We determine the dependence of key inertial confinement fusion (ICF) hot spot properties on the deuterium-tritium (DT) fuel adiabat accomplished by addition of heat to the cold shell. Our main result is to observe that variation of this parameter reduces the simulation to experiment discrepancy in several experimentally inferred quantities. Simulations are continued from capsule only 1D simulations using the Lawrence Livermore National Laboratory ICF code, HYDRA. The continuations employ the high energy density physics (HEDP) University of Chicago code, FLASH, and a hydro only code, FronTier, modified with a radiation equation of state (EOS) model. Hot spot densities, burn-weighted ion temperatures and pressures show a decreasing trend, while the hot spot radius shows an increasing trend in response to added heat to the cold shell. Instantaneous quantities are assessed at the time of maximum neutron production within each simulation.

We present our main conclusions regarding the simulation of turbulent mixing, with a summary of previous results and the inclusion of new evidence in support of these conclusions.Our main conclusions are:1. Turbulent simulations in the Large Eddy Simulation (LES) regime are inherently non-unique, and require experimental validation before they can be used for scientific or engineering purposes.2. The level of non-uniqueness is mesh dependent, decreasing to zero as the mesh is refined. The rate of decrease is slow and governed by Kolmogorov exponents when in a scaling regime.3. Simulation uncertainty is greatly reduced by the use of subgrid scale (SGS) models. For mixing problems (in the case of small time scales or small diffusion parameters), tracking of discontinuities or steep gradients is also essential.4. Simulation codes have implicitly defined subgrid scale terms within them; each new code or code revision needs its own validation study. For the same reason, higher order subgrid terms, or even summing the missing parts of the Kolmogorov spectrum to reconstruct more exact subgrid terms is not a panacea, and validation (adjustment) of subgrid models is still needed. Within our own validation experiments, we find that low order SGS terms, second order differencing and front tracking (to control excess diffusion) result, basically, in a perfect fit to experimental data. That is, no further tuning is required for this algorithm.5. Experimental validation (essential) can be performed at a high but experimentally feasible Reynolds number (Re), followed by an extrapolation to Reynolds numbers needed for engineering design or scientific studies.6. Convergence of the cumulative distribution functions (CDFs) is important for reactive chemistry coupled to turbulent mixing. We provide a mathematical framework for this convergence, and show that it does occur, with slow rates influenced by Kolmogorov exponents.Engineering simulations are often regarded as interpolative, not predictive, in their dependence on experimental data. Our conclusions both support this view and indicate a mitigation strategy based on mesh refinement and the appropriate choice of numerical methods.

Mix is a critical input to hydro simulations used in modeling chemical or nuclear reaction processes in fluids. It has been identified as a possible cause of performance degradation in inertial confinement fusion (ICF) targets. Mix contributes to numerical solution uncertainty through its dependence on turbulent transport coefficients, themselves uncertain and even controversial quantities. These coefficients are a central object of study in this paper, carried out in an Richtmyer–Meshkov unstable circular two-dimensional (2D) geometry suggested by an ICF design. We study a pre-turbulent regime and a fully developed regime. The former, at times between the first shock passage and reshock, is characterized by mixing in the form of interpenetrating but coherent fingers and the latter, at times after reshock, has fully developed turbulent structures. This paper focuses on the scaling of spatial averages of turbulence coefficients under mesh refinement and under variation of molecular viscosity [i.e., Reynolds number (Re)]. We find that the coefficients scale under mesh refinement with a power of spatial grid spacing derived from the Kolmogorov 2/3 law, especially after reshock. We document the dominance of turbulent over molecular transport and convergence of the turbulent transport coefficients in the infinite Re limit. The transport coefficients do not coincide for the pre- and post-reshock flow regimes, with significantly stronger transport coefficients after reshock.

A22 Austenitic chromium-nickel steels with special alloying additions Alkaline Earth Hydroxides A. Metallic materials A. Weser, A. Weser DECHEMA e. V., GermanySearch for more papers by this authorGundula Jänsch-Kaiser, Gundula Jänsch-Kaiser DECHEMA e. V., GermanySearch for more papers by this authorDavid H. Sharp, David H. Sharp Society of Chemical Industry, UKSearch for more papers by this author A. Weser, A. Weser DECHEMA e. V., GermanySearch for more papers by this authorGundula Jänsch-Kaiser, Gundula Jänsch-Kaiser DECHEMA e. V., GermanySearch for more papers by this authorDavid H. Sharp, David H. Sharp Society of Chemical Industry, UKSearch for more papers by this author First published: 07 August 2014 https://doi.org/10.1002/9783527610433.chb243028 Read the full textAbout ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References 1 Rabald, E., Corrosion Guide, p. 133, Elsevier Publishing Company, Amsterdam-London-New York, 1968 Google Scholar Corrosion HandbookBrowse other articles of this reference work:BROWSE BY TOPIC ReferencesRelatedInformation