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At least 523 records · Page 29

Polychromatic Arm Exponents for the Critical Planar FK-Ising Model

Schramm–Loewner evolution (SLE) is a one-parameter family of random planar curves introduced by Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models. This is the only possible process with conformal invariance and a certain “domain Markov property”. In 2010, Chelkak and Smirnov proved the conformal invariance of the scaling limits of the critial planar FK-Ising model which gave the convergence of the interface to SLE{sub 16/3}. We derive the arm exponents of SLE{sub κ} for κ∈(4,8). Combining with the convergence of the interface, we derive the arm exponents of the critical FK-Ising model. We obtain six different patterns of boundary arm exponents and three different patterns of interior arm exponents of the critical planar FK-Ising model on the square lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unruh effect in vacua with anisotropic scaling: Applications to multilayer graphene

We extend the calculation of the Unruh effect to the universality classes of quantum vacua obeying topologically protected invariance under anisotropic scaling r→br, t→b{sup z}t. Two situations are considered. The first one is related to the accelerated detector which detects the electron–hole pairs. The second one is related to the system in external electric field, when the electron–hole pairs are created due to the Schwinger process. As distinct from the Unruh effect in relativistic systems (where z=1) the calculated radiation is not thermal, but has properties of systems in the vicinity of quantum criticality. The vacuum obeying anisotropic scaling can be realized, in particular, in multilayer graphene with the rhombohedral stacking. Opportunities of the experimental realization of the Unruh effect in this situation are discussed. -- Highlights: •Unruh effect in the system with anisotropic scaling (multilayer graphene) is investigated. •The accelerated detector is considered which detects the electron–hole pairs. •The system in external electric field is considered as the “accelerated vacuum”. •Unruh effect in the nonrelativistic case differs from that of the relativistic case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach

Abstract A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates, and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer, rely on the assumption of statistical homogeneity or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique because of a gauge freedom. Here, it is argued that a Galilean-invariant subfilter-scale (SFS) flux is a suitable quantity to properly measure energy scale transfer in the ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale transfer of energy. The paper presents geographic maps of the energy scale transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions near the Gulf Stream and in the Equatorial Countercurrent have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extratropical energy scale transfer over regions of O(103) km in size.

54 ENVIRONMENTAL SCIENCES↗

Cosmological particle production and pairwise hotspots on the CMB

Heavy particles with masses much bigger than the inflationary Hubble scale H * , can get non-adiabatically pair produced during inflation through their couplings to the inflaton. If such couplings give rise to time-dependent masses for the heavy particles, then following their production, the heavy particles modify the curvature perturbation around their locations in a time-dependent and scale non-invariant manner. This results into a non-trivial spatial profile of the curvature perturbation that is preserved on superhorizon scales and eventually generates localized hot or cold spots on the CMB. We explore this phenomenon by studying the inflationary production of heavy scalars and derive the final temperature profile of the spots on the CMB by taking into account the subhorizon evolution, focusing in particular on the parameter space where pairwise hot spots (PHS) arise. When the heavy scalar has an $\mathscr{O}$(1) coupling to the inflaton, we show that for an idealized situation where the dominant background to the PHS signal comes from the standard CMB fluctuations themselves, a simple position space search based on applying a temperature cut, can be sensitive to heavy particle masses M o /H * ~$\mathscr{O}$(100). The corresponding PHS signal also modifies the CMB power spectra and bispectra, although the corrections are below (outside) the sensitivity of current measurements (searches).

79 ASTRONOMY AND ASTROPHYSICS↗

Exploring precipitation pattern scaling methodologies and robustness among CMIP5 models

Pattern scaling is a well-established method for approximating modeled spatial distributions of changes in temperature by assuming a time-invariant pattern that scales with changes in global mean temperature. We compare two methods of pattern scaling for annual mean precipitation (regression and epoch difference) and evaluate which method is better in particular circumstances by quantifying their robustness to interpolation/extrapolation in time, inter-model variations, and inter-scenario variations. Both the regression and epoch-difference methods (the two most commonly used methods of pattern scaling) have good absolute performance in reconstructing the climate model output, measured as an area-weighted root mean square error. We decompose the precipitation response in the RCP8.5 scenario into a CO 2 portion and a non-CO 2 portion. Extrapolating RCP8.5 patterns to reconstruct precipitation change in the RCP2.6 scenario results in large errors due to violations of pattern scaling assumptions when this CO 2 -/non-CO 2 -forcing decomposition is applied. As a result, the methodologies discussed in this paper can help provide precipitation fields to be utilized in other models (including integrated assessment models or impacts assessment models) for a wide variety of scenarios of future climate change.

54 ENVIRONMENTAL SCIENCES↗

Scaling similarities and quasinormal modes of D0 black hole solutions

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit. The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T 9/5 . We also present a similar argument for all other Dp-brane geometries. We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an Ad S2+9/5 × S 8 geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Neural-Network Object-Recognition Program

HONTIOR computer program implements third-order neural network exhibiting invariance under translation, change of scale, and in-plane rotation. Invariance incorporated directly into architecture of network. Only one view of each object needed to train network for two-dimensional-translation-invariant recognition of object. Also used for three-dimensional-transformation-invariant recognition by training network on only set of out-of-plane rotated views. Written in C language.

Spirkovska, L.↗

Impact of Resolution on Simulation of Closed Mesoscale Cellular Convection Identified by Dynamically Guided Watershed Segmentation

Organized mesoscale cellular convection (MCC) is a common feature of marine stratocumulus that forms in response to a balance between mesoscale dynamics and smaller scale processes such as cloud radiative cooling and microphysics. We use the Weather Research and Forecasting model with chemistry (WRF-Chem) and fully coupled cloud-aerosol interactions to simulate marine low clouds during the VOCALS-REx campaign over the southeast Pacific. A suite of experiments with 3- and 9-km grid spacing indicates resolution-dependent behavior. The simulations with finer grid spacing have smaller liquid water paths and cloud fractions, while cloud tops are higher. The observed diurnal cycle is reasonably well simulated. To isolate organized MCC characteristics we develop a new automated method, which uses a variation of the watershed segmentation technique that combines the detection of cloud boundaries with a test for coincident vertical velocity characteristics. This ensures that the detected cloud fields are dynamically consistent for closed MCC, the most common MCC type over the VOCALS-REx region. We demonstrate that the 3-km simulation is able to reproduce the scaling between horizontal cell size and boundary layer height seen in satellite observations. However, the 9-km simulation is unable to resolve smaller circulations corresponding to shallower boundary layers, instead producing invariant MCC horizontal scale for all simulated boundary layers depths. The results imply that climate models with grid spacing of roughly 3 km or smaller may be needed to properly simulate the MCC structure in the marine stratocumulus regions.

58 GEOSCIENCES↗

Constraints on violation of Lorentz invariance from atmospheric showers initiated by multi-TeV photons

Parameterizing hypothetical violation of Lorentz invariance at high energies using the framework of effective quantum field theory, we discuss its effect on the formation of atmospheric showers by very-high-energy gamma rays. In the scenario where Lorentz invariance violation leads to a decrease of the photon velocity with energy the formation of the showers is suppressed compared to the Lorentz invariant case. Absence of such suppression in the high-energy part of spectrum of the Crab nebula measured independently by HEGRA and H.E.S.S. collaborations is used to set lower bounds on the energy scale of Lorentz invariance violation. These bounds are competitive with the strongest existing constraints obtained from timing of variable astrophysical sources and the absorption of TeV photons on the extragalactic background light. They will be further improved by the next generation of multi-TeV gamma-ray observatories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higher-Order Neural Networks Applied to 2D and 3D Object Recognition

A Higher-Order Neural Network (HONN) can be designed to be invariant to geometric transformations such as scale, translation, and in-plane rotation. Invariances are built directly into the architecture of a HONN and do not need to be learned. Thus, for 2D object recognition, the network needs to be trained on just one view of each object class, not numerous scaled, translated, and rotated views. Because the 2D object recognition task is a component of the 3D object recognition task, built-in 2D invariance also decreases the size of the training set required for 3D object recognition. We present results for 2D object recognition both in simulation and within a robotic vision experiment and for 3D object recognition in simulation. We also compare our method to other approaches and show that HONNs have distinct advantages for position, scale, and rotation-invariant object recognition. The major drawback of HONNs is that the size of the input field is limited due to the memory required for the large number of interconnections in a fully connected network. We present partial connectivity strategies and a coarse-coding technique for overcoming this limitation and increasing the input field to that required by practical object recognition problems.

Spirkovska, Lilly↗

Dynamics of Subsiding Shells in Actively Growing Clouds with Vertical Updrafts

The dynamics of a subsiding shell at the edges of actively growing shallow cumulus clouds with updrafts is analyzed using direct numerical simulation. The actively growing clouds have a fixed in-cloud buoyancy and velocity. Turbulent mixing and evaporative cooling at the cloud edges generate a subsiding shell that grows with time. A self-similar regime is observed for first- and second-order moments when normalized with respective maximum values. Internal scales derived from integral properties of the flow problem are identified. A self-similarity analysis using these scales reveals that contrary to classical self-similar flows, the turbulent kinetic energy budget terms and velocity moments scale according to the buoyancy and not with the mean velocity. The shell thickness is observed to increase linearly with time. The buoyancy scale remains time invariant and is set by the initial cloud–environment thermodynamics. The shell accelerates ballistically with a magnitude set by the saturation value of the buoyancy of the cloud–environment mixture. In this regime, the shell is buoyancy driven and independent of the in-cloud velocity. Relations are obtained for predicting the shell thickness and minimum velocities by linking the internal scales with external flow parameters. The values thus calculated are consistent with the thickness and velocities observed in typical shallow cumulus clouds. The entrainment coefficient is a function of the initial state of the cloud and the environment, and is shown to be on the same order of magnitude as fractional entrainment rates calculated for large-scale models.

54 ENVIRONMENTAL SCIENCES↗

Disformal invariance of curvature perturbation

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.

79 ASTRONOMY AND ASTROPHYSICS↗

Neural networks for data compression and invariant image recognition

An approach to invariant image recognition (I2R), based upon a model of biological vision in the mammalian visual system (MVS), is described. The complete I2R model incorporates several biologically inspired features: exponential mapping of retinal images, Gabor spatial filtering, and a neural network associative memory. In the I2R model, exponentially mapped retinal images are filtered by a hierarchical set of Gabor spatial filters (GSF) which provide compression of the information contained within a pixel-based image. A neural network associative memory (AM) is used to process the GSF coded images. We describe a 1-D shape function method for coding of scale and rotationally invariant shape information. This method reduces image shape information to a periodic waveform suitable for coding as an input vector to a neural network AM. The shape function method is suitable for near term applications on conventional computing architectures equipped with VLSI FFT chips to provide a rapid image search capability.

Gardner, Sheldon↗

Final Report: Optimal Model Complexity in Geological Carbon Sequestration: A Response Surface Uncertainty Analysis

The critical component of a risk assessment study in evaluating GCS is an analysis of uncertainty in CO2 modeling. In such analyses, direct numerical simulation of CO2 flow and leakage requires many time-consuming model runs. Alternatively, analytical methods have been developed which allow fast and efficient estimation of CO2 storage and leakage, although restrictive assumptions on formation rock and fluid properties are employed. In this study, an intermediate approach is proposed based on the Design of Experiment and Response Surface methodology, which consists of using a limited number of numerical simulations to estimate a prediction outcome as a combination of the most influential uncertain site properties. The methodology can be implemented within a Monte Carlo framework to efficiently assess parameter and prediction uncertainty while honoring the accuracy of numerical simulations. The choice of the uncertain properties is flexible and can include geologic parameters that influence reservoir heterogeneity, engineering parameters that influence gas trapping and migration, and reactive parameters that influence the extent of fluid/rock reactions. The method was tested and verified on modeling long-term CO2 flow, non-isothermal heat transport, and CO2 dissolution storage by coupling two-phase flow with explicit miscibility calculation using an accurate equation of state that gives rise to convective mixing of formation brine variably saturated with CO2. All simulations were performed using three-dimensional high-resolution models including a target deep saline aquifer, overlying caprock, and a shallow aquifer. To evaluate the uncertainty in representing reservoir permeability, sediment hierarchy of a heterogeneous digital stratigraphy was mapped to create multiple irregularly shape stratigraphic models of decreasing geologic resolutions: heterogeneous (reference), lithofacies, depositional environment, and a (homogeneous) geologic formation. To ensure model equivalency, all the stratigraphic models were successfully upscaled from the reference heterogeneous model for bulk flow and transport predictions (Zhang & Zhang, 2015). GCS simulation was then simulated with all models, yielding insights into the level of parameterization complexity that is needed for the accurate simulation of reservoir pore pressure, CO2 storage, leakage, footprint, and dissolution over both short (i.e., injection) and longer (monitoring) time scales. Important uncertainty parameters that impact these key performance metrics were identified for the stratigraphic models as well as for the heterogeneous model, leading to the development of reduced/simplified models at lower characterization cost that can be used for the reservoir uncertainty analysis. All the CO2 modeling was conducted using PFLOTRAN – a massively parallel, multiphase, multi-component, and reactive transport simulator developed by a multi-laboratory DOE/SciDAC (Scientific Discovery through Advanced Computing) project (Zhang et al., 2017, in review). Within the uncertainty analysis framework, increasing reservoir depth were investigated to explore its effect on the uncertainty outcomes and the potential for developing gravity-stable injection with increased storage security (Dai et al., 20126; Dai et al., 2017, in review). Finally, to accurately model CO2 fluid-rock reactions and resulting long-term storage as secondary carbonate minerals, a modified kinetic rate law for general mineral dissolution and precipitation was proposed and verified that is invariant to a scale transformation of the mineral formula weight. This new formulation will lead to more accurate assessment of mineral storage over geologic time scales (Lichtner, 2016).

58 GEOSCIENCES↗

Constraining Lorentz Invariance Violation Using the Crab Pulsar Emission Observed up to TeV Energies by MAGIC

Spontaneous breaking of Lorentz symmetry at energies on the order of the Planck energy or lower is predicted by many quantum gravity theories, implying non-trivial dispersion relations for the photon in vacuum. Consequently, gamma-rays of different energies, emitted simultaneously from astrophysical sources, could accumulate measurable differences in their time of flight until they reach the Earth. Such tests have been carried out in the past using fast variations of gamma-ray flux from pulsars, and more recently from active galactic nuclei and gamma-ray bursts. We present new constraints studying the gamma-ray emission of the galactic Crab Pulsar, recently observed up to TeV energies by the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) collaboration. A profile likelihood analysis of pulsar events reconstructed for energies above 400 GeV finds no significant variation in arrival time as their energy increases. Ninety-five percent CL limits are obtained on the effective Lorentz invariance violating energy scale at the level of E{sub QG{sub 1}}>5.5×10{sup 17} GeV (4.5×10{sup 17} GeV) for a linear, and E{sub QG{sub 2}}>5.9×10{sup 10} GeV (5.3×10{sup 10} GeV) for a quadratic scenario, for the subluminal and the superluminal cases, respectively. A substantial part of this study is dedicated to calibration of the test statistic, with respect to bias and coverage properties. Moreover, the limits take into account systematic uncertainties, which are found to worsen the statistical limits by about 36%–42%. Our constraints would have been much more stringent if the intrinsic pulse shape of the pulsar between 200 GeV and 400 GeV was understood in sufficient detail and allowed inclusion of events well below 400 GeV.

79 ASTRONOMY AND ASTROPHYSICS↗

Combined convective and diffusive simulations: VERB-4D comparison with 17 March 2013 Van Allen Probes observations: VERB-4D

Our study focused on understanding the coupling between different electron populations in the inner magnetosphere and the various physical processes that determine evolution of electron fluxes at different energies. Observations during the 17 March 2013 storm and simulations with a newly developed Versatile Electron Radiation Belt-4D (VERB-4D) are presented. This analysis of the drift trajectories of the energetic and relativistic electrons shows that electron trajectories at transitional energies with a first invariant on the scale of ~100 MeV/G may resemble ring current or relativistic electron trajectories depending on the level of geomagnetic activity. Simulations with the VERB-4D code including convection, radial diffusion, and energy diffusion are presented. Sensitivity simulations including various physical processes show how different acceleration mechanisms contribute to the energization of energetic electrons at transitional energies. In particular, the range of energies where inward transport is strongly influenced by both convection and radial diffusion are studied. Our results of the 4-D simulations are compared to Van Allen Probes observations at a range of energies including source, seed, and core populations of the energetic and relativistic electrons in the inner magnetosphere.

58 GEOSCIENCES↗