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Results for “conformal differential geometry”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Classical geometries defined by exterior differential systems on higher frame bundles

Exterior differential ideals are discussed, and sets of invariant generators presented, for Reimannian, conformal and projective geometries, and for specializations such as Ricci-flat, self-dual and Einstein-Maxwell theories. The Cartan characteristic integers are explicitly calculated, and involutory basis forms found, for each of these (specialized to four dimensions), exposing their algebraic structure and showing how they generate well-posed sets of partial differential equations.

Estabrook, Frank B.↗
DOE OSTI2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1980

Numerical grid generation techniques

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Source record↗
DOE OSTI2022

Calabi-Yau CFTs and random matrices

Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and the quintic, we show that the spectrum, averaged over a region in complex structure moduli space, possesses the same statistical properties as the Gaussian orthogonal ensemble of random matrix theory.

superstring vacua↗
DOE OSTI2021

4-manifolds and topological modular forms

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Bootstrap bounds on closed Einstein manifolds

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Tailoring Corrosion Resistance of Additively Manufactured Metals with Atomic Layer Deposition

The goal of this work is to develop a scalable post-manufacturing capability at LANL that utilizes atomic layer deposition (ALD) for corrosion-resistant coatings onto additively manufactured (AM) metals. This will provide fundamentally new and essential capabilities towards the interchangeability of AM metals with traditionally wrought or machined material. This will be accomplished by (1) formulating novel ALD precursor doses and film thicknesses onto as-printed coupons of AM metals and (2) providing electrochemical characterization of corrosion susceptibility as a function of deposited film thickness. While ALD is well-established, the unique aspect (risk) of this work is application to rough AM surfaces. This risk is mitigated by repeating ALD deposition cycles, where thicker coatings laterally branch, resulting in a uniform coating. This risk will be assessed in the phase 1 feasibility study, wherein the application of ALD coatings to small AM coupon surfaces will be demonstrated using existing hardware and characterization tools at Sigma. This study alone will provide ground-breaking insight on the compatibility of ALD coating techniques with AM metals. Going beyond the phase 1 study, a standalone deposition chamber will be built, so full AM components can be coated and tested. While this MFR investment is focused on corrosion mitigation, it is critical to highlight external benefits of this technique outside the scope of this proposed study. ALD has extraordinary universality, whereby almost any material can be given almost any coating or graded density coating with atomic precision; and, the only limiting factors to scalability is the size of the dosing chamber. The self-limiting reactions intrinsic to ALD offers high conformity to part geometry and tolerance, even for internal surfaces where electroplating or conventional chemical vapor deposition falls short due to differential diffusion. This uniquely positions ALD at the forefront of post-manufacturing strategies for AM components, especially for those with complex geometry and internal surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Hyperbolic vacua in Minkowski space

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Toward Improved Charge Separation through Conformational Control in Copper Coordination Complexes

The continued development of solar energy as a renewable resource necessitates the design and study of new approaches to sustaining photodriven charge separation (CS). To this end, we present a bioinspired approach in which triggered conformational changes are used to control electron transfer (ET) events. We report, photo-induced conformational rearrangements of a ligand are translated into changes in the coordination geometry and environment about a bound metal ion. Taking advantage of the differential coordination properties of Cu I and Cu II , these dynamics facilitate intramolecular ET from Cu I to the ligand to create a CS state. The synthesis and photophysical characterization of CuCl(dpaa R ) (dpaa = dipicolylaminoacetophenone, with R = H and OMe) is presented. These ligands incorporate a fluorophore into their framework that gives rise to a twisted intramolecular charge transfer (TICT) excited state. Excited state ligand twisting provides a tetragonal coordination geometry capable of capturing Cu II in the CS state when an internal ortho-OMe binding site is present (as in dpaaOMe). We employ NMR, IR, EPR, and optical spectroscopies, X-ray diffraction, and electrochemical methods to establish the ground state properties of the Cu I and Cu II complexes. We then investigate the photophysical dynamics of these Cu I complexes via time-resolved photoluminescence (TR-PL), and optical transient absorption (OTA) spectroscopies. We show that relative to controls lacking a TICT-active ligand, the lifetime of the CS state is enhanced ~1000-fold. Further, the presence of the ortho-OMe substituent greatly enhances the lifetime of the TICT* state and biases the coordination environment toward Cu II . The presence of Cu I decreases photoinduced degradation from 14 to <2% but does not result in significant quenching via ET. Factors affecting CS in these systems are discussed, laying the groundwork for our strategy toward solar energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Celestial leaf amplitudes

Celestial amplitudes may be decomposed as weighted integrals of AdS 3 -Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A new framework for higher loop Witten diagrams

The differential representation is a novel formalism for studying boundary correlators in (d + 1)-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of operator-valued integrals. We use the differential representation to compute three-point bubble and triangle Witten diagrams with external states of conformal dimension ∆ = d. We compare the former to a position space computation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The TESS-Keck Survey. III. A Stellar Obliquity Measurement of TOI-1726 c

We report the measurement of a spectroscopic transit of TOI-1726c, one of two planets transiting a G-type star with V = 6.9 in the Ursa Major Moving Group (∼400 Myr). With a precise age constraint from cluster membership, TOI-1726 provides a great opportunity to test various obliquity excitation scenarios that operate on different timescales. By modeling the Rossiter–McLaughlin (RM) effect, we derived a sky-projected obliquity of −1{sub −32}{sup +35{sup ∘}}. This result rules out a polar/retrograde orbit and is consistent with an aligned orbit for planet c. Considering the previously reported, similarly prograde RM measurement of planet b and the transiting nature of both planets, TOI-1726 tentatively conforms to the overall picture that compact multitransiting planetary systems tend to have coplanar, likely aligned orbits. TOI-1726 is also a great atmospheric target for understanding differential atmospheric loss of sub-Neptune planets (planet b 2.2 R {sub ⊕} and c 2.7 R {sub ⊕} both likely underwent photoevaporation). The coplanar geometry points to a dynamically cold history of the system that simplifies any future modeling of atmospheric escape.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

42 ENGINEERING↗
DOE OSTI2025

Kinematic flow from the flow of cuts

The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic flow, expressed using a set of differential forms referred to as the cut basis, from a geometric perspective, relying solely on the cosmological hyperplane arrangement and without invoking bulk physics. Each element of the cut basis corresponds to the positive geometry associated to an independent cut of the physical FRW-form and can be labeled by decorating (minors of) the truncated Feynman graph with an acyclic orientation. We provide a straightforward prescription to associate a logarithmic differential form to each element of the cut basis by considering its corresponding decorated graph. Moreover, we show that the residues of the physical FRW-form are canonical forms of certain graphical zonotopes labeled by the same set of decorated graphs. These zonotopes control the cut combinatorics -- flow of cuts -- of the physical FRW-form and the cut basis (by construction). Using the theory of relative twisted cohomology and intersection theory, we derive a closed form formula for the differential equations of the cut basis. We also introduce combinatorial rules that compute the kinematic differential of any basis element without explicit calculation. The combinatorics of our differential equations is a natural consequence of the flow of cuts and is equivalent (up to rescaling) to the kinematic flow for the recently studied time integral basis. In particular, our differential equations decouple into exponentially many sectors, one for each way of cutting a subset of edges of the graph.

General Relativity and Quantum Cosmology↗
DOE OSTI2020

Differentiating and Quantifying Gas-Phase Conformational Isomers Using Coulomb Explosion Imaging

Conformational isomerism plays a crucial role in defining the physical and chemical properties and biological activity of molecules ranging from simple organic compounds to complex biopolymers. However, it is often a significant challenge to differentiate and separate these isomers experimentally as they can easily interconvert due to their low rotational energy barrier. Here, we use the momentum correlation of fragment ions produced after inner-shell photoionization to distinguish conformational isomers of 1,2-dibromoethane (C 2 H 4 Br 2 ). We demonstrate that the three-body breakup channel, C 2 H 4 + + Br + + Br + , contains signatures of both sequential and concerted breakup, which are decoupled to distinguish the geometries of two conformational isomers and to quantify their relative abundance. The sensitivity of our method to quantify these yields is established by measuring the relative abundance change with sample temperature, which agrees well with calculations. Finally, our study paves the way for using Coulomb explosion imaging to track subtle molecular structural changes.

Photoionization↗