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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Impact of Pressure-Dependent Interfacial Tension and Contact Angle on Capillary Heterogeneity Trapping of CO2 in Storage Aquifers

Summary Carbon dioxide (CO2) capillary trapping increases the total amount of CO2 that can be effectively immobilized in storage aquifers. This trapping, manifesting itself as accumulated CO2 columns at a continuum scale, is because of capillary threshold effects that occur below low-permeability barriers. Considering that capillary pressure is dictated by heterogeneous pore throat size, the trapped CO2 column height and associated CO2 saturation will vary spatially within a storage aquifer. This variation will be influenced by two pressure-dependent interfacial parameters—CO2/brine interfacial tension (IFT) and CO2/brine/rock contact angle. Our objective is to understand how the pressure dependence of these two parameters affects the heterogeneity of capillary trapped CO2 at a continuum scale. Our conceptual model is a 1D two-zone system with the upper zone being a flow barrier (low permeability) and the lower zone being a flow path (high permeability). The inputs to this model include microfacies-dependent capillary pressure vs. saturation curves and permeability values. The input capillary pressure curves were collected in the literature that represents carbonate microfacies (e.g., dolograinstone) in a prevalent formation in the Permian Basin. We then used the Leverett j-function to scale the capillary pressure curve for the two zones that are assigned with the same or different microfacies. During scaling, we considered the influence of pressure on both the IFT and contact angle of CO2/brine/dolomite systems. We varied the zone permeability contrast ratio from 2 to 50. We then assumed capillary gravity equilibriums and calculated the CO2 saturation buildup corresponding to various trapped CO2 column heights. The CO2 saturation buildup is defined as the CO2 saturation in the lower layer minus that in the upper one. We found that the saturation buildup can be doubled when varying pressure in a storage aquifer, after considering pressure-dependent IFT and contact angles. Thus, assuming these two parameters to be constant across such aquifers would cause large errors in the quantification of capillary trapping of CO2. The whole study demonstrates the importance of considering pressure-dependent interfacial properties in predicting the vertical distribution of capillary trapped CO2. It has important implications in developing a better understanding of leakage risks and consequent storage safety.

Engineering↗
DOE OSTI2021

A test of the standard cosmological model with geometry and growth

We perform a general test of the ΛCDM and wCDM cosmological models by comparing constraints on the geometry of the expansion history to those on the growth of structure. Specifically, we split the total matter energy density, Ω M , and (for wCDM) dark energy equation of state, w, into two parameters each: one that captures the geometry, and another that captures the growth. We constrain our split models using current cosmological data, including type Ia supernovae, baryon acoustic oscillations, redshift space distortions, gravitational lensing, and cosmic microwave background (CMB) anisotropies. We focus on two tasks: (i) constraining deviations from the standard model, captured by the parameters ΔΩ M ≡ Ω M grow -Ω M geom and Δw ≡ w grow -w geom , and (ii) investigating whether the S 8 tension between the CMB and weak lensing can be translated into a tension between geometry and growth, i.e. ΔΩ M ≠ 0, Δw ≠ 0. In both the split ΛCDM and wCDM cases, our results from combining all data are consistent with ΔΩ M = 0 and Δ w = 0. If we omit BAO/RSD data and constrain the split wCDM cosmology, we find the data prefers Δw < 0 at 3.6σ significance and ΔΩ M > 0 at 4.2σ evidence. We also find that for both CMB and weak lensing, ΔΩ M and S 8 are correlated, with CMB showing a slightly stronger correlation. Furthermore, the general broadening of the contours in our extended model does alleviate the S 8 tension, but the allowed nonzero values of ΔΩ M do not encompass the S 8 values that would point toward a mismatch between geometry and growth as the origin of the tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Supersymmetric Wilson loops on the lattice in the large N limit

We propose additional tests of holography by studying supersymmetric Wilson loops in p+1-dimensional maximally supersymmetric Yang?Mills (SYM) theories on the lattice in the large N limit. In the dual gravity description, this computation involves calculating the area of a fundamental string worldsheet in certain Type II supergravity backgrounds. Though thermodynamic observables have been computed on the lattice using Monte Carlo methods and agree with the supergravity results in various dimensions, not much has been done for the gauge-invariant operators such as the Wilson loop. We provide analytical predictions for these loops for various non-conformal Dp-brane background cases with ? ? 2 p?2 in the large N limit and comment on how these can be computed on non-orthogonal lattices in various models.

Jha, Raghav G. (ORCID:0000000329330102)↗
DOE OSTI2020

Convergent evolution of tree hydraulic traits in Amazonian habitats: implications for community assemblage and vulnerability to drought

Amazonian droughts are increasing in frequency and severity. However, little is known about how this may influence species-specific vulnerability to drought across different ecosystem types. We measured 16 functional traits for 16 congeneric species from six families and eight genera restricted to floodplain, swamp, white-sand or plateau forests of Central Amazonia. We investigated whether habitat distributions can be explained by species hydraulic strategies, and if habitat specialists differ in their vulnerability to embolism that would make water transport difficult during drought periods. We found strong functional differences among species. Nonflooded species had higher wood specific gravity and lower stomatal density, whereas flooded species had wider vessels, and higher leaf and xylem hydraulic conductivity. The P 50 values (water potential at 50% loss of hydraulic conductivity) of nonflooded species were significantly more negative than flooded species. However, we found no differences in hydraulic safety margin among species, suggesting that all trees may be equally likely to experience hydraulic failure during severe droughts. Water availability imposes a strong selection leading to differentiation of plant hydraulic strategies among species and may underlie patterns of adaptive radiation in many tropical tree genera. Our results have important implications for modeling species distribution and resilience under future climate scenarios.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Spectral form factor in sparse SYK models

We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value of N out of reach of current numerical simulations.

2D Gravity↗
DOE OSTI2020

Black hole echoes

In this work, we consider a very simple model for gravitational wave echoes from black hole merger ringdowns which may arise from local Lorentz symmetry violations that modify graviton dispersion relations. If the corrections are sufficiently soft so they do not remove the horizon, the reflection of the infalling waves which trigger the echoes is very weak. As an example, we look at the dispersion relation of a test scalar field corrected by rotonlike operators depending only on spatial momenta, in Gullstrand-Painlevé coordinates. The near-horizon regions of a black hole do become reflective, but only very weakly. The resulting “bounces” of infalling waves can yield repetitive gravity wave emissions but their power is very small. This implies that to see any echoes from black holes we really need an egregious departure from either standard GR or effective field theory, or both. One possibility to realize such strong echoes is the recently proposed classical firewalls which replace black hole horizons with material shells surrounding timelike singularities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Comparative Analysis of Pendulum and Flywheel Power Take-Off Mechanisms for Wave Energy Conversion

Here, this study compares three power-take-off (PTO) mechanisms for wave energy converters—a flywheel -type pitch resonator and two pendulum variants (normal and inverted)—all designed to fit within a fixed envelope. Performance is assessed via linear frequency-domain models and bi-conjugate impedance matching under a representative sea state. The inverted-pendulum PTO achieves 27.9% of the incident wave energy, versus 16.5% for the normal pendulum and 4.2% for the flywheel—that is, 6.6 × and 3.9 × improvements, respectively. These gains arise because pendulum-based systems generate higher torque for a given buoy motion and maintain impedance matching across a wider frequency band. Parametric studies of mass, pendulum arm length, spring stiffness, generator friction, and motor constant quantify the impact of key design choices on power output. By locating the pendulum pivot near the buoy's center of gravity and positioning the center of rotation below the COG, surge–pitch coupling is improved and energy transfer is further boosted.

Keow, Alicia Li Jen [Sandia National Laboratories ↗
DOE OSTI2020

Design and Development of a Robotic Exoskeleton Device for use in Glove Boxes - 20374

Glovebox operators in nuclear facilities often operate under radioactive environment and typically perform monotonous, dull and repetitive work. This can result in muscle fatigue leading to increased levels of accidents. Current research work aims in assisting the glovebox operators by designing a novel upper limb exoskeleton device to reduce injuries and increase worker efficiency. Almost none of the commercially available hand and upper body exoskeletons are directly suitable for use in gloveboxes. This explains the novelty of the present work in developing a wearable powered robotic exoskeleton device. The device consists of electronics, motors and spring systems mounted on adjustable plates and is supported by a stationary frame behind the worker. The device is intended to be portable and adjustable according to the operator height. The elbow has a flexion movement assisted with motor control by way of a Bowden cable system. The system is floated on a spring and pulley combination that allows for extra safety and smoothness of operation. The end points are fixed near the pivot points to help minimize unwanted movement/torque. The extension movement of the upper and lower arm are assisted by gravity and a counter spring. The shoulder and upper arm movement are held in a neutral position with a spring system for counter balance allowing small movements within the glovebox. This initial concept considers only the vertical movement of the arm. The abduction and adduction movement will not be assisted or impeded by the over shoulder plate or at the forearm plate allowing for full range of motion. Several glovebox aspects such as the level of task assistance, ergonomic design, minimum hindrance in dexterity/operator movements and tear resistance for hazardous safety reasons will be considered in the design of the exoskeleton. Computer models will be simulated to test the load levels and stress conditions on the exoskeleton to enhance the designs. The exoskeleton focusses on major muscular involvement reduction through weight offset and active assistance with minimal parts and hence the device is derived with several joint links and contains both passive and active joints. The paper details the various stages in the design development and prototype testing of the exoskeleton device. Upon successful prototype device development, human testing will be conducted in a replica of the SRS-235F hot cell facility constructed at FIU-ARC. The final stage of the project will be potential testing/deployment of the exoskeleton device in one of the glovebox facilities in Savannah River Nuclear Waste site. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Resurgence, conformal blocks, and the sum over geometries in quantum gravity

In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, R) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements

We present cosmological results from the measurement of clustering of galaxy, quasar and Lyman-α forest tracers from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). We adopt the full-shape (FS) modeling of the power spectrum, including the effects of redshift-space distortions, in an analysis which has been thoroughly validated in a series of supporting papers as summarised in [1]. We combine the full-shape information with DESI's DR1 constraints from the baryon acoustic oscillations (BAO) of these tracers. In the flat ΛCDM cosmological model, DESI (FS+BAO), combined with a baryon density prior from Big Bang Nucleosynthesis and a weak prior on the scalar spectral index, determines matter density to Ω m = 0.2962 ± 0.0095, and the amplitude of mass fluctuations to σ 8 = 0.842 ± 0.034. The addition of the cosmic microwave background (CMB) data tightens these constraints to Ω m = 0.3056 ± 0.0049 and σ 8 = 0.8121 ± 0.0053, while further addition of the joint clustering and lensing analysis from the Dark Energy Survey Year-3 (DESY3) data further improves these measurements, and leads to a 0.4% determination of the Hubble constant, H 0 = (68.40 ± 0.27) km s -1 Mpc -1 . In models with a time-varying dark energy equation of state parametrised by w 0 and w a , combinations of DESI (FS+BAO) with CMB and type Ia supernovae continue to show the preference, previously found in the DESI DR1 BAO analysis, for w 0 > -1 and w a < 0 with similar levels of significance. DESI data, in combination with the CMB, improve the upper limits on the sum of the neutrino masses relative to the case when only the DR1 BAO was available, giving ∑m ν < 0.071 eV at 95% confidence. We finally constrain deviations from general relativity represented by two modified gravity parameters. DESI (FS+BAO) data alone measure the parameter that controls the clustering of massive particles, μ 0 = 0.11 +0.45 -0.54 , in agreement with the zero value predicted by general relativity. The combination of DESI with the CMB and the clustering and lensing analysis from DESY3 constrains both modified-gravity parameters, giving μ 0 = 0.04 ± 0.22 and Σ 0 = 0.044 ± 0.047, again in agreement with general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The Last Journey. I. An Extreme-scale Simulation on the Mira Supercomputer

The Last Journey is a large-volume, gravity-only, cosmological N-body simulation evolving more than 1.24 trillion particles in a periodic box with a side length of 5.025 Gpc. It was implemented using the HACC simulation and analysis framework on the BG/Q system Mira. The cosmological parameters are chosen to be consistent with the results from the Planck satellite. A range of analysis tools have been run in situ to enable a diverse set of science projects and, at the same time, keep the resulting data amount manageable. Analysis outputs have been generated starting at redshift z ~ 10 to allow for construction of synthetic galaxy catalogs using a semianalytic modeling approach in postprocessing. As part of our in situ analysis pipeline, we employ a new method for tracking halo substructures, introducing the concept of subhalo cores. The production of multiwavelength synthetic sky maps is facilitated by generating particle light cones in situ, also beginning at z ~ 10. We provide an overview of the simulation setup and generated data products; a first set of analysis results is presented. A subset of the data is publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An Educational Guide for 2D Stellar Structure Calculations of Rapidly Rotating Stars using the ESTER code

The Evolution STEllaire en Rotation (ESTER) code is the first 2D stellar structure code to be made open-source and freely available to the astronomy and astrophysics community. An important and novel advancement of this code is that it can reproduce the distorted shape and observable signatures (e.g., gravity darkening) of rapidly rotating stars. ESTER also calculates the steady-state large-scale flows within the star, namely their differential rotation and associated meridional circulation. In this report, we explore and document the physics implemented within version 1.1.0rc2 of the ESTER code, in a way that complements published descriptions. We illustrate this physics by plotting how stellar structure parameters vary through stellar interiors at a range of latitudes and at different angular velocities. We investigate how the thin convective envelopes of intermediate mass stars vary with latitude when rapidly rotating, becoming deeper and thicker near the equator. Simple comparisons of ESTER model predictions (e.g., central temperature and density, luminosity) with the output from the Modules for Experiments in Stellar Astrophysics (MESA) code [Paxton et al., 2010] shows generally good agreement. Additional comparisons provide important benchmarking and verification for ESTER as a comparatively young code. Finally, we provide a guide for installing and running the code on our local university cluster, aimed at helping students to begin work.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Geothermal play fairway analysis, part 1: Example from the Snake River Plain, Idaho

The Snake River Plain (SRP) volcanic province overlies the track of the Yellowstone hotspot, a thermal anomaly that extends deep into the mantle. Most of the area is underlain by a basaltic volcanic province that overlies a mid-crustal intrusive complex, which in turn provides the long-term heat flux needed to sustain geothermal systems. Previous studies have identified several known geothermal resource areas within the SRP. For the geothermal study presented herein, our goals were to: (1) adapt the methodology of Play Fairway Analysis (PFA) for geothermal exploration to create a formal basis for its application to geothermal systems, (2) assemble relevant data for the SRP from publicly available and private sources, and (3) build a geothermal PFA model for the SRP and identify the most promising plays, using GIS-based software tools that are standard in the petroleum industry. The study focused on identifying three critical resource parameters for exploitable hydrothermal systems in the SRP: heat source, reservoir and recharge permeability, and cap or seal. Data included in the compilation for heat source were heat flow, distribution and ages of volcanic vents, groundwater temperatures, thermal springs and wells, helium isotope anomalies, and reservoir temperatures estimated using geothermometry. Reservoir and recharge permeability was inferred from the analysis of stress orientations and magnitudes, post-Miocene faults, and subsurface structural lineaments based on magnetics and gravity data. Data for cap or seal included the distribution of impermeable lake sediments and clay-seal associated with hydrothermal alteration below the regional aquifer. These data were used to compile Common Risk Segment maps for heat, permeability, and seal, which were combined to create a Composite Common Risk Segment map for all southern Idaho that reflects the risk associated with geothermal resource exploration and identifies favorable resource tracks. Our regional assessment indicated that undiscovered geothermal resources may be located in several areas of the SRP. Two of these areas, the western SRP and Camas Prairie, were selected for more detailed assessment, during which heat, permeability, and seal were evaluated using newly collected field data and smaller grid parameters to refine the location of potential resources. These higher resolution assessments illustrate the flexibility of our approach over a range of scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Quantum complexity in gravity, quantum field theory, and quantum information science

Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. Here, we seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.

Baiguera, Stefano [Istituto Nazionale di Fisica Nu↗
DOE OSTI2022

Detailed Chemical Abundances for a Benchmark Sample of M Dwarfs from the APOGEE Survey

Individual chemical abundances for 14 elements (C, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, and Ni) are derived for a sample of M dwarfs using high-resolution, near-infrared H-band spectra from the Sloan Digital Sky Survey-IV/Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. The quantitative analysis included synthetic spectra computed with 1D LTE plane-parallel MARCS models using the APOGEE Data Release 17 line list to determine chemical abundances. The sample consists of 11 M dwarfs in binary systems with warmer FGK dwarf primaries and 10 measured interferometric angular diameters. To minimize atomic diffusion effects, [X/Fe] ratios are used to compare M dwarfs in binary systems and literature results for their warmer primary stars, indicating good agreement (<0.08 dex) for all studied elements. The mean abundance difference in primaries minus this work's M dwarfs is –0.05 ± 0.03 dex. It indicates that M dwarfs in binary systems are a reliable way to calibrate empirical relationships. A comparison with abundance, effective temperature, and surface gravity results from the APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP) Data Release 16 finds a systematic offset of [M/H], T eff , log g = +0.21 dex, –50 K, and 0.30 dex, respectively, although ASPCAP [X/Fe] ratios are generally consistent with this study. The metallicities of the M dwarfs cover the range of [Fe/H] = –0.9 to +0.4 and are used to investigate Galactic chemical evolution via trends of [X/Fe] as a function of [Fe/H]. The behavior of the various elemental abundances [X/Fe] versus [Fe/H] agrees well with the corresponding trends derived from warmer FGK dwarfs, demonstrating that the APOGEE spectra can be used to examine Galactic chemical evolution using large samples of selected M dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Tidally Excited Modes and δ Scuti Pulsations in the Eclipsing Triple Star IM Persei

IM Per is a triple star system whose eclipsing pair masses and radii are accurate to within 1%. The Transiting Exoplanet Survey Satellite (TESS) light curve of the program target exhibits partial eclipses and multiple oscillations with millimagnitude-level amplitudes. It is found that the oscillations affect eclipse timing measurements. Binary modeling of the high-quality TESS data indicates that the eclipsing components of the triple system are twin dwarfs with parameters of M {sub 2}/M {sub 1} = 0.995, R {sub 2}/R {sub 1} = 0.901, and Δ(T{sub eff,1}–T{sub eff,2}) = 12 K in an eccentric (e = 0.049), detached configuration. The third light of l {sub 3} = 0.054 may mostly come from a G-type tertiary companion. Our predicted parallax of 1.52 ± 0.09 mas is concurrent with the Gaia measurement of 1.52 ± 0.05 mas. Multifrequency analysis of the outside-eclipse residuals reveals 22 significant pulsation signals: 4 in the gravity-mode region (0.03−2.22 day{sup −1}) and 18 in the pressure-mode region (9.19−25.12 day{sup −1}). Of the low frequencies, f {sub 11} and f {sub 14} are orbital harmonics that can be identified as tidally excited modes. The pulsation periods and constants for the high frequencies, and the position in the Cepheid instability strip demonstrate that the pulsating component of IM Per is a δ Sct variable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Gravitational production of completely dark photons with nonminimal couplings to gravity

Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗