Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1|2) "Dirac square root" of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical BRST operator. The theory is a basic ingredient for building fundamental theories of physical observables.Comment: 4 pages, LaTe

Quantum Darboux theorem

The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wave functions. In this picture, the base manifold is an odd-dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime,"while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem"that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial

Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 1. Regular Shock Refraction

Shock refraction is a fundamental shock phenomenon observed when shocks interact with a material interface separating gases with different properties. Following refraction, a transmitted shock enters the second gas and a reflected wave returns back into the first gas. In the case of regular shock refraction, all of the waves meet at a single point called the triple-point, creating five different states for the two gases. Analytical methods based on shock polar analysis have been developed to determine the state of two ideal gases in each of the five refraction regions. Furthermore, shock refraction constitutes a basic example of complex hydrodynamic flows. For this reason, shock refraction is used in this report as one validation of the high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method, as implemented in the HOPE code. The algorithms used in the HOPE code are described in detail, together with its current capabilities. The following two-step validation process is adopted. First, analytical results are obtained for the normal and oblique shock refraction (with shock-interface angle {beta}{sub interface} = 75{sup o}) observed for a Ma = 1.2 shock. To validate the single-fluid and the two-fluid implementations of the WENO method, two pairs of gases, argon/xenon, having equal adiabatic exponents {gamma} and air(acetone)/sulfur hexafluoride, having different adiabatic exponents, are considered. Both the light-to-heavy and heavy-to-light gas configurations are considered. Second, numerical simulations are performed using the fifth-order WENO method and values of the density, pressure, temperature, speed of sound, and flow velocity in each of the five refraction regions are compared with the analytical predictions obtained from shock polar analysis. In all of the cases considered, excellent agreement is found between the simulation results and the analytical predictions. The results from this investigation suggest that the WENO method is a very useful numerical method for the simulation and modeling of complex hydrodynamic flows

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability. I. Comparison to experimental data and to amplitude growth model predictions

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially non-oscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF{sub 6} shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical and phenomenological linear and nonlinear, impulsive, perturbation and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Pade model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically. In Part II [Phys. Fluids (2006)], a comprehensive investigation of mixing induced by the reshocked single-mode Richtmyer-Meshkov instability is performed using the present simulation data to assess and quantify the effects of reshock and other waves on the mixing dynamics, including the post-reshock growth, circulation deposition, mixing profiles and fractions, baroclinic circulation deposition, energy spectra and statistics

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability

Finite-difference weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform spatial grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, chemical products and mixing fractions, energy spectra, statistics, probability distribution functions, effective turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and effective numerical viscosity on the order and resolution is comprehensively investigated to long evolution times. The results are interpreted using the computed implicit numerical diffusion arising from the truncation errors in the characteristic projection-based WENO method. It is quantitatively shown that simulations with higher order and higher resolution have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition on the evolving interface by the second shock-interface interaction induces the formation of small-scale structures. Simulations using lower orders of reconstruction and on coarser grids preserve large-scale structures and flow symmetry to late times, while simulations using higher orders of reconstruction and on finer grids exhibit fragmentation of the structures, symmetry breaking and increased mixing. The investigation demonstrates that similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than doubling the resolution for the complex shock-driven hydrodynamic flow and WENO method considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities

Assessment of gradient-diffusion closures for modeling Rayleigh-Taylor and Richtmyer-Meshkov instability-induced mixing

The validity of gradient-diffusion closures for modeling turbulent transport in multi-mode Rayleigh-Taylor and reshocked Richtmyer-Meshkov instability-induced mixing is investigated using data from three-dimensional spectral/tenth-order compact difference and ninth-order weighted essentially non-oscillatory simulations, respectively. Details on the numerical methods, initial and boundary conditions, and validation of the results are discussed elsewhere [2, 3]. First, mean and fluctuating fields are constructed using spatial averaging in the two periodic flow directions. Then, quantities entering eddy viscosity-type gradient-diffusion closures, such as the turbulent kinetic energy and its dissipation rate (or turbulent frequency), and the turbulent viscosity are constructed. The magnitudes of the terms in the turbulent kinetic energy transport equation are examined to identify the dominant processes. It is shown that the buoyancy (or shock) production term is the dominant term in the transport equation, and that the shear production term is relatively small for both the Rayleigh-Taylor and Richtmyer-Meshkov cases. Finally, a priori tests of gradient-diffusion closures of the unclosed terms in the turbulent kinetic energy transport equation are performed by comparing the terms constructed directly using the data to the modeled term. A simple method for estimating the turbulent Schmidt numbers appearing in the closures is proposed. Using these turbulent Schmidt numbers, it is shown that both the shape and magnitude of the profiles of the dominant terms in the turbulent kinetic energy transport equation across the mixing layer are generally well captured

Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability

The ninth-order weighted essentially non-oscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air(acetone)/SF{sub 6} shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike perturbation amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock [Latini, Schilling and Don, Phys. Fluids (2007), in press]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe reshock. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney and Zabusky [J. Fluid Mech. 269, 45 (1994)] model and linear instability theory. The time-evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the circulations are equal before, as well as after reshock, until the interaction of the reflected rarefaction with the layer leads to flow symmetry breaking and different evolutions of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in very good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and molecular mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating entropy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops non-trivial spectral content from its inception. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing, followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction approaches unity across the layer at the latest time, signifying nearly complete mixing. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra are consistent with most of these scalings over short wave number ranges. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is shown that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field

Natural control of Helicoverpa armigera (Lepidoptera: Noctuidae) pupae in organic and conventional maize crops.

The natural biological control of soil pests is poorly studied. Notably, the control of Helicoverpa armigera in the pupae stage is unknown. To increase knowledge about the control of this pest in organic and conventional maize crop, tests were conducted to verify if the duration of pupae availability in days, the type of crop treatment (organic and conventional), the stage of crop development, and the depth of the soil significantly affect predation by natural enemies. The pupae availability time (days) in the soil did not affect their removal by natural enemies. However, in the fallow stage, on the surface and in the reproductive phase, the predation was higher. In organic maize, predation was 15% higher when compared to conventional maize. The rupture of the soil and the possible losses associated with beneficial fauna were the main factors responsible for higher predation during fallow, so conservationist practices usually used in organic treatment are the main reason for higher predation in this type of crop. There is a significant decrease in the control of H. armigera pests by natural enemies when maize is grown using conventional practices, what reinforces the importance of the conservation techniques used in maize crop

Richtmyer-Meshkov instability-induced mixing: initial conditions modeling, three-dimensional simulations and comparisons to experiment

Turbulent transport and mixing in the reshocked multi-mode Richtmyer-Meshkov instability is investigated using three-dimensional ninth-order weighted essentially non-oscillatory simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF{sub 6} Vetter-Sturtevant [1] experiment. The mass fraction isosurfaces and density cross-sections show the detailed structure before, during, and after reshock. The effects of reshock are quantified using the baroclinic enstrophy production, buoyancy production, and shear production terms. The mixing layer growth agrees well with the experimental growth rate. The post-reshock growth is in good agreement with the Mikaelian reshock model [2]

A Single-Center Retrospective Analysis of 14 Head and Neck AVMs Cases Treated with a Single-Day Combined Endovascular and Surgical Approach

Arteriovenous malformations (AVMs) are rare congenital defects of vascular development whose treatment remains challenging. The paper presents a retrospective single-center study of 14 patients with AVMs of the head and neck region undergoing combined endovascular and surgical treatment in a single day. AVM architecture and therapeutic strategies were determined on the basis of angiographic studies, while the psychological involvement of each patient was assessed by means of a questionnaire. Most of the 14 patients achieved satisfactory clinical results with no recurrences, good aesthetic and functional results, and most patients reported improved quality of life. The combined endovascular and surgical approach is an effective treatment for AVMs of the head and neck and performing it on the same day is a possible option often accepted by patients which guarantees operative advantages for the surgeon