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At least 55 records · Page 3

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗

The effect of rigid electron rotation on the Grad–Shafranov equilibria of a class of FRC devices

Rigid electron rotation of a Rotamak-FRC produces a pressure flux function that is more peaked than the Solov'ev flux function. This paper explores the implications of this peaked pressure flux function, including the isothermal case, which appear when the temperature profile is broader than the density profile, creating both benefits and challenges to a Rotamak-FRC based fusion reactor. In this regime, the density distribution becomes very peaked, enhancing the fusion power. The separatrix has a tendency to become oblate, which can be mitigated by flux conserving current loops. Plasma extends outside the separatrix, notably in the open field line region. Furthermore, this model does not apply to very kinetic FRCs or FRCs in which there are significant ion flows, but it may have some applicability to their outer layers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

Abstract We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved—or to account for chemical reactions, non-conserved—currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in–in formalism on the Schwinger–Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales—much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction–diffusion equations as a final coherence check.

Mechanics↗

IR side of bounds on theories with spontaneously broken Lorentz symmetry

In nature, some UV features of dynamics are reflected in IR quantities. In fully relativistic theories, this connection can be probed through the analyticity properties of scattering amplitudes, allowing one to understand which IR theories respect the UV assumptions of quantum field theory. The ensuing analyticity bounds can usually be rephrased as the absence of faster-than-light propagation for low-energy excitations. While it is interesting to understand these relations and their IR characterization for theories that have less idealized properties, it is also more difficult to derive analyticity bounds in these cases. For theories that spontaneously break Lorentz symmetry, recent progress was made by considering correlators of conserved currents and their analyticity properties. In this work, we focus on such theories and work to close the gap from the IR side, finding a natural way to express the known analyticity bounds purely in terms of low-energy kinematical quantities. Our analysis shows that the bounds require gapped excitations to have a slower speed than the gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to interpret the UV/IR connection in more complex theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Causal and stable first-order chiral hydrodynamics

We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a U ( 1 ) V conserved current or a U ( 1 ) A current with a chiral anomaly or both. Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. We present our results in a form amenable to numerical hydrodynamic simulations. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Impossible symmetries and conformal gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity.

79 ASTRONOMY AND ASTROPHYSICS↗

Improving Dose Modeling With Dynamic Modeling Tools [Slides]

Utilities aiming for higher fuel enrichment for power uprates or extended operation times before refueling must conduct a new dose analysis. Current conservative dose estimation standards may cause utilities to exceed regulatory limits for proposed increased fuel enrichment. A more accurate modeling of doses from reactor accidents can lower these conservative assumptions. Prescott et al. (2022) demonstrated that the Event Modeling Risk Assessment using Linked Diagrams (EMRALD) software tool, developed at Idaho National Laboratory (INL), can be coupled with the Modular Accident Analysis Program (MAAP5) for dynamic accident analysis in reactor plants. EMRALD forms models of potential accident scenarios, while MAAP5 simulates the accident progression and dose consequences. By integrating these software tools with utility-specific data, a more precise estimation of dose consequences from plant accidents can be achieved. Preliminary findings indicate that EMRALD provides accurate mean core damage frequencies for generalized accident scenarios. Future work includes expanding the model to account for plant-specific data and mitigation factors.

97 - MATHEMATICS AND COMPUTING↗

Electrostatic model of a quiet auroral arc

The physics and equations used in the proposed electrostatic model of a quiet auroral arc are discussed. The procedure for obtaining approximate solutions of Poisson's equation coupled to ionosphere current conservation is given. A comparison with a specific discrete auroral arc as seen from the auroral satellite S3-3 is presented.

Chiu, Y. T.↗

A multigrid solver for the semiconductor equations

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

Bachmann, Bernhard↗

Non-Noetherian symmetries for oscillators in classical mechanics and in field theory

Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.

Hojman, Sergio A.↗

Central Park Ecological Conservation: Assessing Tree Health Conditions in New York City’s Central Park with NASA Earth Observation Data

The Central Park Conservancy stewards New York City’s iconic Central Park with a mission to preserve the park for all. This mission is complicated by the spread of Dutch elm disease (DED) which has threatened the culturally and ecologically significant American elm tree (Ulmus americana). Central Park is home to one of the largest and last remaining urban concentrations of American elm and the Conservancy currently protects them through integrated pest management. This paper discusses an interdisciplinary feasibility study that assessed the application of NASA Earth observations from 2014 to 2023 to detect changes in forest phenology possibly related to DED. Landsat 8 and 9 imagery was used to calculate multiyear time series of the Normalized Difference Vegetation Index (NDVI) and quantify changes in land surface phenology for a given year. A pixel-based logistic regression analysis was performed using changes in NDVI, tree site locations, and recorded occurrences of trees infected with DED as inputs. The results of this analysis show that changes in NDVI derived from Landsat data are capable of detecting unhealthy tree canopies with 71% precision and healthy tree canopies with 41% precision. The study had uncertainties and limitations due to the spatial and temporal resolutions of Landsat, the natural variability in land surface phenology and NDVI, and the attempt to detect disease impacts while disease prevention and mitigation is occurring. As is, the findings of this study and its methods provide managers with an approach for integrating Earth observations to make more informed decisions in the application and timing of urban forest management activities.

Central Park↗

Assessing Tree Health Conditions in New York City’s Central Park with Earth Observation Data

The Central Park Conservancy stewards New York City’s iconic Central Park with a mission to preserve the park for all. This mission is complicated by the spread of Dutch elm disease (DED) which has threatened the culturally and ecologically significant American elm tree (Ulmus americana). Central Park is home to one of the largest and last remaining urban concentrations of American elm and the Conservancy currently protects them through integrated pest management. This project is an interdisciplinary feasibility study that assessed the application of NASA Earth observations from 2014 to 2023 to detect changes in forest phenology possibly related to DED. Landsat 8 and 9 imagery was used to calculate a multiyear time series of the Normalized Difference Vegetation Index (NDVI) and quantify changes in land surface phenology. A pixel-based logistic regression analysis was performed using changes in NDVI, tree site locations, and recorded occurrences of trees infected with DED as inputs. The results of this analysis show that changes in NDVI derived from Landsat data are capable of detecting unhealthy tree canopies with 71% precision and healthy tree canopies with 41% precision. The study had uncertainties and limitations due to the spatial and temporal resolutions of Landsat, the natural variability in land surface phenology and NDVI, and the attempt to detect disease impacts while disease prevention and mitigation are occurring. As is, the findings of this study and its methods provide managers with an approach for integrating Earth observations to make more informed decisions in the application and timing of urban forest management activities.

John Hocknell↗

Most Probable Fire Scenarios in Spacecraft and Extraterrestrial Habitats: Why NASA's Current Test 1 Might Not Always Be Conservative

NASA s current method of material screening determines fire resistance under conditions representing a worst-case for normal gravity flammability - the Upward Flame Propagation Test (Test 1[1]). Its simple pass-fail criteria eliminates materials that burn for more than 12 inches from a standardized ignition source. In addition, if a material drips burning pieces that ignite a flammable fabric below, it fails. The applicability of Test 1 to fires in microgravity and extraterrestrial environments, however, is uncertain because the relationship between this buoyancy-dominated test and actual extraterrestrial fire hazards is not understood. There is compelling evidence that the Test 1 may not be the worst case for spacecraft fires, and we don t have enough information to assess if it is adequate at Lunar or Martian gravity levels.

Olson, S. L.↗

Most Probable Fire Scenarios in Spacecraft and Extraterrestrial Habitats: Why NASA's Current Test 1 Might Not Always be Conservative

NASA's current method of material screening determines fire resistance under conditions representing a worst-case for normal gravity flammability - the Upward Flame Propagation Test (Test 1). Its simple pass-fail criteria eliminates materials that burn for more than 12 inches from a standardized ignition source. In addition, if a material drips burning pieces that ignite a flammable fabric below, it fails. The applicability of Test 1 to fires in microgravity and extraterrestrial environments, however, is uncertain because the relationship between this buoyancy-dominated test and actual extraterrestrial fire hazards is not understood. There is compelling evidence that the Test 1 may not be the worst case for spacecraft fires, and we don t have enough information to assess if it is adequate at Lunar or Martian gravity levels.

Olson, S. L.↗

Momentum-exchange current drive by electrostatic waves in an unmagnetized collisionless plasma

For a planar electrostatic wave interacting with a single species in a collisionless plasma, momentum conservation implies current conservation. However, when multiple species interact with the wave, they can exchange momentum, leading to current drive. A simple, general formula for this driven current is derived. As examples, we show how currents can be driven for Langmuir waves in electron–positron–ion plasmas, and for ion-acoustic waves in electron–ion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-Order Space-Time Methods for Conservation Laws

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

Huynh, H. T.↗