Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sigma models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Topology of the $O(3)$ non-linear sigma model under the gradient flow

The $O(3)$ non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, featuring topological qualities. Though the topological susceptibility should vanish in physical theories, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$.

Thomas, Stuart↗
NASA NTRS1994

Development and initial test of the University of Wisconsin global isentropic-sigma model

The description of a global version of the University of Wisconsin (UW) hybrid isentropic-sigma (theta-sigma) model and the results from an initial numerical weather prediction experiment are presented in this paper. The main objectives of this initial test are to (1) discuss theta-sigma model development and computer requirements, (2) demonstrate the ability of the UW theta-sigma model for global numerical weather prediction using realistic orography and parameterized physical processes, and (3) compare the transport of an inert trace constituent against a nominally 'identical' sigma coordinate model. Initial and verifying data for the 5-day simulations presented in this work were supplied by the Goddard Earth Observing System (GEOS-1) data assimilation system. The time period studied is 1-6 February 1985. This validation experiment demonstrates that the global UW theta-sigma model produces a realistic 5-day simulation of the mass and momentum distributions when compared to both the identical sigma model and GEOS-1 verification. Root-mean-square errors demonstrate that the theta-sigma model is slightly more accurate than the nominally identical sigma model with respect to standard synoptic variables. Of particular importance, the UW theta-sigma model displays a distinct advantage over the conventional sigma model with respect to the prognostic simulation of inert trace constituent transport in amplifying baroclinic waves of the extratropics. This is especially true in the upper troposphere and stratosphere where the spatial integrity and conservation of an inert trace constituent is severely compromised in the sigma model compared to the theta-sigma model.

Zapotocny, Tom H.↗
DOE OSTI2025

Ordinary and exotic mesons in the extended Linear Sigma Model

The extended Linear Sigma Model (eLSM) is a hadronic model based on the global symmetries of QCD and the corresponding explicit, anomalous, and spontaneous breaking patterns. In its basic three-flavor form, its mesonic part contains the dilaton/glueball as well as the nonets of pseudoscalar, scalar, vector, and axial–vector mesons, thus chiral symmetry is linearly realized. In the chiral limit and neglecting the chiral anomaly, only one term – within the dilaton potential – breaks dilatation invariance, and all terms are chirally symmetric. Spontaneous symmetry breaking is implemented by a generalization of the Mexican-hat potential, with explicit symmetry breaking responsible for its tilting. The overall mesonic phenomenology up to ~2 GeV is in agreement with the PDG compilation of masses and partial and total decay widths. The eLSM was enlarged in a straightforward way to include other conventional quark–antiquark nonets (pseudovector and orbitally excited vector mesons, tensor and axial-tensor mesons, radially excited (pseudo)scalar mesons, etc.), as well as two nonets of hybrid mesons, the lightest one with exotic quantum numbers J $\mathscr{PC}$ = 1 -+ not allowed for $\bar{q}q$ objects, such as the resonance π 1 (1600) and the recently discovered η 1 (1855) . In doing so, different types of chiral multiplets are introduced: heterochiral and homochiral multiplets, which differ in the way they transform under chiral transformations. Moreover, besides the scalar glueball that is present from the beginning as dilaton, other glueballs, the tensor, the pseudoscalar and the vector glueballs were coupled to the eLSM: the scalar resonance ƒ 0 (1710) turns out to be mostly gluonic, the tensor glueball couples strongly to vector mesons, and the pseudoscalar glueball couples sizably to $ππη'$ and can be assigned to X (2370) or X (2600). In all cases above, masses and decays can be analyzed allowing for a better understanding of both conventional and non-conventional mesons: whenever data are available, a comparison is performed and, when this is not the case, predictions of decay widths and decay ratios are outlined. The eLSM contains chiral partners on an equal footing and is therefore well suited for studies of chiral symmetry restoration at nonzero temperature and densities: this is done by coupling it to the Polyakov loop. Finally, the QCD phase diagram and the location of the critical endpoint were investigated within this framework.

Chiral symmetry↗
DOE OSTI2024

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking

We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional “geometric” results obtained in the background field methods, in this way resolving the peculiarities pointed out in O. Gamayun et al. [Peculiarities of beta functions in sigma models, J. High Energy Phys. 10 (2023) 097]. The result is achieved by the supersymmetric completion of the first-order sigma model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

A comparison of regional isentropic-sigma and sigma model simulations of the January 1979 Chicago blizzard

In an initial effort in regional numerical weather prediction, results from the University of Wisconsin isentropic-sigma (UW theta-sigma) hybrid model and an 'identical' sigma model are compared. The two main objectives are to demonstrate the capability of the UW theta-sigma model for regional numerical weather prediction and to identify advantages of the hybrid model in simulating atmospheric water vapor transport and precipitation relative to the sigma model. The 72-h simulations produced by the two models extend over a region covering the western Pacific Ocean, North America, and the western Atlantic Ocean. The simulations begin at 0000 UTC 13 January 1979, a period during which an intense Chicago blizzard develops over the central United States. This period also includes the rapid development of a cyclone in the western Pacific Ocean. Results using the Global Weather Experiment (GWE) ECMWF level IIIB data as initial and verification data indicate that both models produce reasonable and similar 72-h simulations, with the UW theta-sigma model mass and momentum distributions being slightly more accurate than the sigma model. Of particular importance for the Chicago blizzard is that the UW theta-sigma model more accurately simulates water vapor transport northward from the Gulf of Mexico and westward from the Atlantic Ocean. As a result, the hybrid model more accurately simulates observed precipitation, especially over the northeastern U.S. and southeastern Canada.

Zapotocny, Tom H.↗
NASA NTRS1989

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Zhang, Shoucheng↗
DOE OSTI2024

Lie-algebraic Kähler sigma models with U(1) isotropy

We discuss various questions that emerge in connection with the Lie-algebraic deformation of the sigma model in two dimensions. First, we supersymmetrize the original model endowing it with the minimal and extended supersymmetries. Then we derive the general hypercurrent anomaly in both cases. In the latter case this anomaly is one-loop but is somewhat different from the standard expressions one can find in the literature because the target manifold is nonsymmetric. We also show how to introduce the twisted masses and the term, and study the Bogomol’nyi–Prasad–Sommerfield equation for instantons, in particular the value of the topological charge. Then we demonstrate that the second loop in the function of the nonsupersymmetric Lie-algebraic sigma model is due to an infrared effect. To this end we use a supersymmetric regularization. We also conjecture that the above statement is valid for higher loops too, similar to the parallel phenomenon in four-dimensional super-Yang-Mills. In the second part of the paper we develop a special dimensional reduction—namely, starting from the two-dimensional Lie-algebraic model we arrive at a quasi-exactly solvable quantum-mechanical problem of the Lamé type.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Peculiarities of beta functions in sigma models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories.

Sigma Models↗
DOE OSTI2024

Infinite Family of Integrable Sigma Models Using Auxiliary Fields

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g , these models include an auxiliary field v α which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor. Published by the American Physical Society 2024

Physics↗
DOE OSTI2025

Non-invertible defects from the Conway SCFT to K3 sigma models. Part I. General results

We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module V f♮ . We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four-plane-preserving TDLs in V f♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.

Conformal Field Models in String Theory↗
NASA NTRS1993

A comparison of simulated precipitation by hybrid isentropic-sigma and sigma models

Simulations of dry and moist baroclinic development from 10- and 22-layer hybrid isentropic-sigma coordinate models are compared with those from 11-, 27-, and 35-layer sigma coordinate models. The ability of the models to transport water vapor and simulate equivalent potential temperature is examined. Predictions of the timing, location, and amount of precipitation are compared. Several analytical distributions of water vapor are specified initially. It is shown that when the relative humidity is vertically uniform through a substantial extent of the atmosphere, all the models produce very similar precipitation distributions. However, when water vapor is confined to relatively shallow layers, the ability of the sigma coordinate models to simulate the timing, location, and amount of precipitation is severely compromised.

Johnson, Donald R.↗
DOE OSTI2025

T Duality and T T ¯ -like Deformations of Sigma Models

We initiate the study of the interplay between T duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T duality commutes with the T T ¯ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T duality and arbitrary T T ¯ -like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T dual are classically integrable. Published by the American Physical Society 2025

Bielli, Daniele (ORCID:0009000640034768)↗
NASA NTRS1991

Numerical investigations with a hybrid isentropic-sigma model. I - Normal-mode characteristics. II - The inclusion of moist processes

The normal-mode characteristics of baroclinically amplifying disturbances were numerically investigated in a series of adiabatic simulations by a hybrid isentropic-sigma model, demonstrating the effect of coupling an isentropic-coordinate free atmospheric domain with a sigma-coordinate PBL on the normal-mode characteristics. Next, the normal-mode model was modified by including a transport equation for water vapor and adiabatic heating by condensation. Simulations with and without a hydrological component showed that the overall effect of latent heat release is to markedly enhance cyclogenesis and frontogenesis.

Pierce, R. B.↗
DOE OSTI2023

Large inflationary logarithms in a nontrivial nonlinear sigma model

Loops of inflationary gravitons are known to induce large temporal and spatial logarithms that can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature that can be reduced to free field theories by local, invertible field redefinitions. Here we study a model that cannot be so reduced and still shows the same sorts of large logarithms. Additionally, we compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop β and γ functions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model

An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

Heller, Urs M.↗
DOE OSTI2025

Integrable higher-spin deformations of sigma models from auxiliary fields

We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parametrized by an interaction function of several variables, which extends the formalism of [C. Ferko and L. Smith, An infinite family of integrable sigma models using auxiliary fields, .] and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality “commutes” with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case. Published by the American Physical Society 2025

Bielli, Daniele (ORCID:0009000640034768)↗
DOE OSTI2024

Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr ( Φ 3 ) theory

Scattering amplitudes for the simplest theory of colored scalar particles—the Tr ( Φ 3 ) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr ( Φ 3 ) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr ( Φ 3 ) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U ( N ) → U ( N − k ) × U ( k ) . The Goldstone amplitudes for this theory coincide with those of pions in the U ( N ) × U ( N ) → U ( N ) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr ( Φ 3 ) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1983

A comparison of methods for computing the sigma-coordinate pressure gradient force for flow over sloped terrain in a hybrid theta-sigma model

In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Johnson, D. R.↗