Obstruction tensors in Weyl geometry and holographic Weyl anomaly
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We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be n s = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of n s , either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r 0.002 < 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V"(Φ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc -1 ≲ k ≲ 0.2 Mpc -1 . A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.
The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone — the holographic entropy cone — in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary number of parties, it is known that the so-called perfect tensors are extreme rays. In this work, we constrain the form of the remaining extreme rays by showing that they correspond to geometries with vanishing mutual information between any two parties, ensuring the absence of Bell pair type entanglement between them. This is tantamount to proving that besides subadditivity, all non-redundant holographic entropy inequalities are superbalanced, i.e. not only do UV divergences cancel in the inequality itself (assuming smooth entangling surfaces), but also in the purification thereof.
Changes in fluid pressure deform porous media and this effect occurs in a variety of hydrogeologic processes, from the change in storage during pumping or injection to fluctuations in water levels caused by barometric pressure. We have developed instruments for measuring small strains in porous media, and we have used the resulting strain data to evaluate well testing, hydraulic fracturing, manual loading at the ground surface, and ambient hydrologic processes, like rainfall and evaporation. A particularly important application is the use of strain tensor data measured at shallow depths to analyze well tests or hydraulic fractures conducted at much greater depths. An early demonstration of this technique was conducted at the North Avant Field north of Tulsa, Oklahoma, where Pennsylvanian sandstone creates a confined aquifer and oil reservoir at a depth of 530m. We have showed that the strains caused by injecting into the aquifer could be measured at a depth of 30m and used to evaluate the properties of the aquifer. We recently expanded the array of strainmeters at the North Avant Field by deploying three more instruments at shallow depth (30m) along with a deep instrument at 520m depth in the winter, 2021. The deep instrument is deployed in shale caprock slightly above the aquifer. To our knowledge, the deep strainmeter at the North Avant Field is the deepest strainmeter ever deployed and this required refining methods originally developed for shallow deployments. The instrument was lowered to depth on oil field tubing and cemented in place using techniques and materials developed for use in oil wells. Optical fiber used to communicate with the instrument was cemented in the annulus on the outside of tubing. This is significant because the techniques we used could readily be extended to greater depth, suggesting that strainmeters can be deployed over a wide range of depths for monitoring critical subsurface processes. For example, it suggests that strainmeters could be deployed through the caprock to monitor for leaks from underlying CO2 storage reservoirs. The strainmeter array at the North Avant Field has been used to characterize deformation during a series of injection tests in the spring and summer, 2021. All the new strainmeters respond to pumping, and the strainmeters we installed earlier also responded. To our knowledge, this is the first application of well testing in a deep aquifer that was monitored by an array of strainmeters—our earlier work used strainmeters at a single location. We are currently analyzing the strain data using an analytical solution, a proxy-based Bayesian inversion algorithm, and other methods. Strainmeter data has also been used to characterize periodic pumping tests by us and Riley Blais. A periodically varying pumping rate causes both hydraulic head and strain signals that vary with the same period as the pumping. The peaks and troughs of the head in monitoring wells lag behind the peaks and troughs of the head in the pumping well, and this lag time increases with distance from the pumping well. The lag time of the pressure and the distance to the monitoring well can be used in a simple analysis to estimate the hydraulic diffusivity of the aquifer. The lag time determined from strain data can be used to estimate aquifer properties using the same analysis that works for the pressure only for strain data measured at particular locations. That is because the strain field in a confining unit advances upward, laterally and then downward even though the pressure in the underlying aquifer only advances laterally, according to our recent simulations. We have field data showing that a small periodic signal superimposed on an injection rate at the North Avant Field will create a periodic strain signal at shallow strainmeters. The field data and the recent simulations suggest that including a periodic component to injection or pumping and then monitoring the resulting strain signal could be a way to monitor the subsurface.
Changes in fluid pressure deform porous media and this effect occurs in a variety of hydrogeologic processes, from the change in storage during pumping or injection to fluctuations in water levels caused by barometric pressure. We have developed instruments for measuring small strains in porous media, and we have used the resulting strain data to evaluate well testing, hydraulic fracturing, manual loading at the ground surface, and ambient hydrologic processes, like rainfall and evaporation. A particularly important application is the use of strain tensor data measured at shallow depths to analyze well tests or hydraulic fractures conducted at much greater depths. An early demonstration of this technique was conducted at the North Avant Field north of Tulsa, Oklahoma, where Pennsylvanian sandstone creates a confined aquifer and oil reservoir at a depth of 530m. We have showed that the strains caused by injecting into the aquifer could be measured at a depth of 30m and used to evaluate the properties of the aquifer. We recently expanded the array of strainmeters at the North Avant Field by deploying three more instruments at shallow depth (30m) along with a deep instrument at 520m depth in the winter, 2021. The deep instrument is deployed in shale caprock slightly above the aquifer. To our knowledge, the deep strainmeter at the North Avant Field is the deepest strainmeter ever deployed and this required refining methods originally developed for shallow deployments. The instrument was lowered to depth on oil field tubing and cemented in place using techniques and materials developed for use in oil wells. Optical fiber used to communicate with the instrument was cemented in the annulus on the outside of tubing. This is significant because the techniques we used could readily be extended to greater depth, suggesting that strainmeters can be deployed over a wide range of depths for monitoring critical subsurface processes. For example, it suggests that strainmeters could be deployed through the caprock to monitor for leaks from underlying CO2 storage reservoirs. The strainmeter array at the North Avant Field has been used to characterize deformation during a series of injection tests in the spring and summer, 2021. All the new strainmeters respond to pumping, and the strainmeters we installed earlier also responded. To our knowledge, this is the first application of well testing in a deep aquifer that was monitored by an array of strainmeters—our earlier work used strainmeters at a single location. We are currently analyzing the strain data using an analytical solution, a proxy-based Bayesian inversion algorithm, and other methods. Strainmeter data has also been used to characterize periodic pumping tests by us and Riley Blais. A periodically varying pumping rate causes both hydraulic head and strain signals that vary with the same period as the pumping. The peaks and troughs of the head in monitoring wells lag behind the peaks and troughs of the head in the pumping well, and this lag time increases with distance from the pumping well. The lag time of the pressure and the distance to the monitoring well can be used in a simple analysis to estimate the hydraulic diffusivity of the aquifer. The lag time determined from strain data can be used to estimate aquifer properties using the same analysis that works for the pressure only for strain data measured at particular locations. That is because the strain field in a confining unit advances upward, laterally and then downward even though the pressure in the underlying aquifer only advances laterally, according to our recent simulations. We have field data showing that a small periodic signal superimposed on an injection rate at the North Avant Field will create a periodic strain signal at shallow strainmeters. The field data and the recent simulations suggest that including a periodic component to injection or pumping and then monitoring the resulting strain signal could be a way to monitor the subsurface.
The Turbomachinery Laboratory at Texas A&M has been providing experimental data and computational codes for the design seals for many years. The program began with the development of a Halon based seal test rig. This facility provided information about the effective stiffness and damping in whirling seals. The Halon effectively simulated cryogenic fluids. Another test facility was developed (using air as the working fluid) where the stiffness and damping matrices can be determined. This data was used to develop bulk flow models of the seal's effect upon rotating machinery; in conjunction with this research, a bulk flow model for calculation of performance and rotordynamic coefficients of annular pressure seals of arbitrary non-uniform clearance for barotropic fluids such as LH2, LOX, LN2, and CH4 was developed. This program is very efficient (fast) and converges for very large eccentricities. Currently, work is being performed on a bulk flow analysis of the effects of the impeller-shroud interaction upon the stability of pumps. The data was used along with data from other researchers to develop an empirical leakage prediction code for MSFC. Presently, the flow field inside labyrinth and annular seals are being studied in detail. An advanced 3-D Doppler anemometer system is being used to measure the mean velocity and entire Reynolds stress tensor distribution throughout the seals. Concentric and statically eccentric seals were studied; presently, whirling seals are being studied. The data obtained are providing valuable information about the flow phenomena occurring inside the seals, as well as a data base for comparison with numerical predictions and for turbulence model development. A finite difference computer code was developed for solving the Reynolds averaged Navier Stokes equation inside labyrinth seals. A multi-scale k-epsilon turbulence model is currently being evaluated. A new seal geometry was designed and patented using a computer code. A large scale, 2-D seal flow visualization facility is also being developed.
Observations of the three-dimensional velocity distributions of positive ions and electrons have been recently gained for the first time in Earth's distant magnetotail with the Galileo and Geotail spacecraft. For this brief discussion of these exciting results the focus is on the overall character of the ion velocity distributions during substorm activity. The ion velocity distributions within and near the magnetotail current sheet are not accurately described as convecting, isotropic Maxwellians. The observed velocity distributions are characterized by at least two robust types. The first type is similar to the 'lima bean'-shaped velocity distributions that are expected from the nonadiabatic acceleration of ions which execute Speiser-type trajectories in the current sheet. The second distribution is associated with the presence of cold ion beams that presumably also arise from the acceleration of plasma mantle ions in the electric and weak magnetic fields in the current sheet. The ion velocity distributions in a magnetic field structure that is similar to that for plasmoids are also examined. Again the velocity distributions are not Maxwellian but are indicative of nonadiabatic acceleration. An example of the pressure tensor within the plasmoid-like event is also presented because it is anticipated that the off-diagonal elements are important in a description of magnetotail dynamics. Thus our concept of magnetotail dynamics must advance from the present assumption of co-moving electron and ion Maxwellian distributions into reformulations in terms of global kinematical models and nonadiabatic particle motion.
A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).
Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTNS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTNS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome lattice.
Large classes of dark sector models feature mass scales and couplings very different from the ones we observe in the Standard Model (SM). Moreover, in the freeze-in mechanism, often employed by the dark sector models, it is also required that the dark sector cannot be populated during the reheating process like the SM. This is the so called asymmetric reheating. Such disparities in sizes and scales often call for dynamical explanations. In this paper, we explore a scenario in which slow evolving conformal field theories (CFTs) offer such an explanation. Building on the recent work on conformal freeze-in (COFI), we focus on a coupling between the Standard Model Hypercharge gauge boson and an anti-symmetric tensor operator in the dark CFT. We present a scenario which dynamically realizes the asymmetric reheating and COFI production. With a detailed study of dark matter production, and taking into account limits on the dark matter (DM) self-interaction, warm DM bound, and constraints from the stellar evolution, we demonstrate that the correct relic abundance can be obtained with reasonable choices of parameters. The model predicts the existence of a dark photon as an emergent composite particle, with a small kinetic mixing also determined by the CFT dynamics, which correlates it with the generation of the mass scale of the dark sector. At the same time, COFI production of dark matter is very different from those freeze-in mediated by the dark photon. This is an example of the physics in which a realistic dark sector model can often be much richer and with unexpected features.
We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.
The physics of ion cyclotron heating (ICH) relevant to the steady-state linear machine MPEX (Material Plasma Exposure eXperiment) has been explored in its predecessor, short-pulse device: Proto-MPEX. MPEX will utilize fundamental ICH to increase heat flux at the target and produce ion temperatures and velocity distributions with improved fidelity to those found in a tokamak divertor region, in comparison to those produced by substrate biasing. In the experiments on Proto-MPEX described here, bulk ion temperatures up to ~15 eV have been achieved with 20 kW net ICH power at 6.5 MHz, using ICH heating of a deuterium plasma produced by a helicon plasma source. The heat flux at the target has been observed to increase throughout the plasma cross section, including in the core region. Core $T_i$ and target heat flux are observed to scale linearly with injected ICH power. Further, measurements of plasma loading and target heat flux as a function of the magnetic field strength at the antenna, together with modeling of the wave propagation from the antenna to the ion cyclotron resonance using the ANTENA and COMSOL codes with a warm plasma dielectric tensor, indicate that power is coupled to the core plasma via fast wave excitation of a kinetic Alfvén wave.
The purpose of this study is to gain a better understanding of the parameters affecting crack growth direction in unidirectional composite materials. To achieve this, the effect of anisotropy and biaxial, far field, loading on the direction of crack growth in unidirectional off-axis composite materials is investigated. Specific emphasis is placed on defining the crack-tip-stress field and finding a consistent criterion for predicting the direction of crack growth. An anisotropic crack-tip-stress analysis was implemented using three criteria (the normal stress ratio theory, the tensor polynomial failure criterion, and the strain energy density theory) to predict the direction of crack extension in unidirectional off-axis graphite-epoxy. The theoretically predicted crack extension directions were then compared with experimental results. It was determined that only the normal stress-ratio criterion correctly predicts the direction of crack extension.
Liquid fuel nuclear reactors offer innovative possibilities in terms of nuclear reactor designs and passive safety systems. Molten Salts Reactors (MSRs) with a fast spectrum are a particular type of these reactors using liquid fuel. MSFRs often involve large open cavities in their core in which the liquid fuel circulates at a high speed to transport the heat generated by the nuclear reactions into the heat exchangers. This high-speed flow yields a turbulent field with large Reynolds numbers in the reactor core. Since the nuclear power, the neutron precursor’s transport and the thermal exchanges are strongly coupled in the MSFR’s core cavity, having accurate turbulent models for the liquid fuel flow is necessary to avoid introducing significant errors in the numerical simulations of these reactors. Nonetheless, high-accuracy simulations of the turbulent flow field in the reactor cavity of these reactors are usually prohibitively expensive in terms of computational resources, especially when performing multiphysics numerical calculations. Therefore, in this work, we propose a novel method using a modified genetic algorithm to optimize the calculation of the Reynolds Shear Stress Tensor (RST) used for turbulence modeling. The proposed optimization methodology is particularly suitable for advanced liquid fuel reactors such as the MSFRs since it allows the development of high-accuracy but still low-computational-cost turbulence models for the liquid fuel. We demonstrate the applicability of this approach by developing high accuracy Reynolds-Averaged Navier–Stokes (RANS) models (averaged flow error less than 5%) for a low and a large aspect ratio in a Backward-Facing Step (BFS) section particularly challenging for RANS models. The newly developed turbulence models better capture the flow field after the boundary layer tipping, over the extent of the recirculation bubble, and near the boundary layer reattachment region in both BFS configurations. The main reason for these improvements is that the developed models better capture the flow field turbulent anisotropy in the bulk region of the BFS. Then, we illustrate the interest in using this turbulence modeling approach for the case of an MSFR by quantifying the impact of the turbulence modeling on the reactor key parameters.
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It is argued that it is appropriate to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyro-radii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies greater than or approximately equal to several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities, L approximately 2 x 10 to the 11th power. Particles with gyro-radii much less than this mean separation (energies less than or approximately equal to 100 MeV/nucleon) appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. For these particles the correlation length is shown to be L approximately 10 to the 10th power cm. With this system of two correlation lengths the cosmic-ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (approximately 50 MeV/nucleon).
A previous paper [Z. Bern et al., Binary dynamics through the fifth power of spin at 𝑂(𝐺 2 ), Phys. Rev. Lett. 130, 201402 (2023)] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through 𝒪(𝛼 2 ) and 𝒪(𝑆 2 ), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity.
This project developed methodologies to measure the in-situ principal stress in the deep subsurface through use of multiple independent, but complementary, seismic methods, laboratory verification, and development of theoretical frameworks. By leveraging existing regional and local datasets we developed, tested, and refined a set of diagnostic tools for determining the in-situ stress state with reduced uncertainty at and below reservoir depths (1.5-6 km). A set of novel tools was produced that are scale independent, such that their utility is equivalent on regional, field scale, and near borehole monitoring of principal stresses in reservoir underburden for carbon storage projects. During a 4-year Department of Energy (DOE) and Southern Company funded project, carried out by the Electric Power Research Institute (EPRI), Lawrence Livermore National Laboratory (LLNL), the University of Oklahoma (OU), and the U.S. Geological Survey (USGS), the project team developed methodologies to measure the far-field in-situ principal stress in the deep subsurface, leveraging induced seismicity data from waste-water disposal projects. These methodologies consisted in the use of well-established and technically advanced seismic processing methods, such as virtual seismometer method-moment tensor (VSM-MT) and shear wave splitting (SWS), that are adept at recovering the stress orientation and certain components of the stress tensor. These methods were applied to robust seismicity catalogs created with matched filter techniques near sites of active fluid disposal—a proxy for carbon storage sites where such datasets are more limited. Estimates of the stress orientation made with seismic processing tools were considered along with laboratory acoustic emission experiments conducted on rock samples from the region of interest. Stress orientations in the studied region do not vary significantly across distances of ~100 km, nor are they found to rotate through time as a consequence of local wastewater disposal, as previously speculated. Finally, the project team investigated the trade-offs among the different seismic methods and evaluated the range of uncertainty that is generated with these methodologies, which led to a practical use and refinement of the VSM-MT technique when it is applied to field datasets. Understanding the trade-offs between these different methods highlighted the potential benefits of improved quantification of uncertainties on stress field estimations.