Integrating Physical Principles with Machine Learning for Predicting Field-Enhanced Catalysis
Not Available
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SEARCH · Engineering Papers
Results for “Integrable field theories”
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.
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Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators
Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The generation of gravitational waves. I - Weak-field sources
This paper derives and summarizes a 'plug-in-and-grind' formalism for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, the formalism reduces to standard 'linearized theory'. Independent of the effects of gravity on the motions, the formalism reduces to the standard 'quadrupole-moment formalism' if the motions are slow and internal stresses are weak. In the general case, the formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime and breaks the Green's function integral into five easily understood pieces: direct radiation, produced directly by the motions of the source; whump radiation, produced by the 'gravitational stresses' of the source; transition radiation, produced by a time-changing time delay ('Shapiro effect') in the propagation of the nonradiative 1/r field of the source; focusing radiation, produced when one portion of the source focuses, in a time-dependent way, the nonradiative field of another portion of the source; and tail radiation, produced by 'back-scatter' of the nonradiative field in regions of focusing.
Thorne, K. S.↗
Model-independent measurement of the Higgs boson associated production with two jets and decaying to a pair of W bosons in proton-proton collisions at $\sqrt{s}=13$ TeV
A model-independent measurement of the differential production cross section of the Higgs boson decaying into a pair of W bosons, with a final state including two jets produced in association, is presented. In the analysis, events are selected in which the decay products of the two W bosons consist of an electron, a muon, and missing transverse momentum. The model independence of the measurement is maximized by employing a discriminating variable, developed through machine learning, that is agnostic to the signal hypothesis. The analysis is based on proton-proton collision data at $\sqrt{s}=13$ TeV collected with the CMS detector from 2016–2018, corresponding to an integrated luminosity of 138 fb −1 . The production cross section is measured as a function of the difference in azimuthal angle between the two jets. The differential cross section measurements are used to constrain Higgs boson couplings within the standard model effective field theory framework.
Hadron-Hadron Scattering↗
Unsteady compressible potential flow around lifting bodies - General theory.
The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green's function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. This representation reduces properly to the lifting surface theories as well as to other classical mathematical formulas. Under small perturbation assumption, the potential at any point P in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integrodifferential equation relating the potential and its normal derivative on the surface of the body.
Morino, L.↗
High speed propeller acoustics and aerodynamics - A boundary element approach
The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.
Farassat, F.↗
Multicentered black hole saddles for supersymmetric indices
The supersymmetric index in string theory can sometimes have a discontinuous integer-valued jump at co-dimension one surfaces in moduli space called walls of marginal stability. When the index counts black hole microstates, crossing such walls of marginal stability amounts to the appearance or disappearance of a large number of such states. While wall-crossing has been understood in string theory and through the disappearance of extremal Lorentzian supergravity solutions as the moduli are varied, there has been no understanding about how the discontinuous changes in the index occur at the level of the gravitational path integral. In this paper, we find the finite-temperature saddles in $4d$ flatspace supergravity in which fermionic fields are periodic when going around the thermal circle that correspond to the multi-center black hole contributions to the index. By analyzing these saddles, we can explain how wall-crossing occurs: as the scalar moduli in supergravity are varied at the asymptotic boundary, for a given split of the charges, the saddle point equations can no longer be solved and, consequently, the corresponding multi-center saddle no longer contributes to the index. While the values of the scalars and the jump in the index when a wall is crossed all agree with the prediction from previously found Lorentzian supergravity solutions, the saddles in the index exhibit a much richer moduli space, which we analyze in detail.
FOS: Physical sciences↗
On the theory of self-focusing of powerful wave beams in nonhomogeneous media
The stationary self-focusing of the Gauss wave beam is considered in a nonhomogeneous medium in the case of local nonlinearity. Equations of the aberrationless approximation for the beam width, the field on the beam axis and the refraction factor are integrated on a computer. Self-focusing in dependence of the nonlinearity level and initial divergence, the dissipation, the length of nonhomogeneity of the dielectric permittivity nondisturbed by a beam, and the diffraction parameter are investigated.
Yerokhin, N. S.↗
Implications of the Landau equations for iterated integrals
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Machine-Assisted Discovery of Integrable Symplectic Mappings
Integrable systems possess a hidden symmetry associated with the existence of conserved quantities known as integrals of motion. These systems play an important role in understanding general dynamics in accelerators and have potential for future designs. This work will cover two automated methods for finding integrable symplectic maps of the plane. The first algorithm is based on the observation that the evolution of an integrable system in phase space is confined to a lower-dimensional submanifold of a specific type. The second algorithm relies on an analysis of dynamical variables. Both methods rediscover some of the famous McMillan-Suris integrable mappings and ultra-discrete Painlev\'e equations. Over 100 new integrable families are presented and analyzed, some of which are isolated in the space of parameters, while others are families with one parameter (or the ratio of parameters) being either continuous or discrete. In addition, the newly discovered maps are related to a general 2D symplectic map through the use of discrete perturbation theory. A method is proposed for constructing smooth near-integrable dynamical systems based on mappings with polygon invariants.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Soft factorisation and exponentiation from Schwinger-space geometry
Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.
Factorization↗
Holography: Quantum Mechanical Aspects of Black Holes (Final Report)
Current theories of fundamental physics are based on quantum field theory, unifying quantum mechanics and special relativity. A similar unification of quantum field theory with gravity has been elusive. String theory is a consistent model of quantum gravity and it is important to identify general lessons that can be applied to the real world. The main technique that emerged from such studies has been the gravitational path integral. During the period of this grant, the PI has explored the implication of the gravitational path integral in novel setups to uncover new features of rotating black holes in four dimensions, as well as increasing our understanding of some specific black holes in string theory.
79 ASTRONOMY AND ASTROPHYSICS↗
The prediction of two-dimensional airfoil stall progression
A generalized boundary condition potential flow calculation method was combined with a momentum integral boundary layer method and a base flow theory of separation to predict airfoil viscous-inviscid interference up to and beyond stall. The resultant program considers laminar and turbulent separation and is, therefore, applicable to thin or thick airfoil stall. The calculated flow field includes the airfoil and the separation bubble recombination region behind the airfoil. Calculated pressure distributions and equivalent airfoil shapes, including the displacement thickness of the viscous regions, are compared with flow field measurements for several airfoils. The measured displacement thicknesses and wake centerlines corroborate the calculated shape. The comparison also suggests the use of the analytical solution to evaluate the measurements.
Gross, L. W.↗
Asymptotic high frequency analysis of the electromagnetic backscattering from an inlet model consisting of piecewise linearly tapered sections
Electromagnetic backscattering from an open ended three dimensional inlet model is analyzed and computed patterns are compared with results of experimental measurements. The model is comprised of two sections. The first section consists of a linearly tapered waveguide with a rectangular opening at one end and the other end is connected to the second section which is a uniform rectangular waveguide with a planar perfectly conducting termination. The model is electrically large so that many propagating modes are excited. The method of analysis contains conventional aperture integration and modal techniques combined with high frequency techniques, which employ concepts such as modal rays, geometrical theory of diffraction and equivalent currents. For the cases considered, it is shown that only a few of the many propagating modes contribute appreciably to the backscattered field. These modes are selected according to their modal ray angle directions.
Altintas, A.↗
Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory
The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Path integral contour deformations for noisy observables
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Field theories with a vector global symmetry
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quasilinear theory for inhomogeneous plasma
Here, this paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the H -theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗