Search NASA⌕ Search

SEARCH · Search NASA

Results for “VERTEX FUNCTIONS”

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 109 records · Page 6

More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve

We perform here exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $\mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. Specifically, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Chiral symmetry breaking with lattice propagators

We study chiral symmetry breaking using the standard gap equation, supplemented with the infrared-finite gluon propagator and ghost dressing function obtained from large-volume lattice simulations. One of the most important ingredients of this analysis is the non-Abelian quark-gluon vertex, which controls the way the ghost sector enters into the gap equation. Specifically, this vertex introduces a numerically crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. This latter quantity satisfies its own, previously unexplored, dynamical equation, which may be decomposed into individual integral equations for its various form factors. In particular, the scalar form factor is obtained from an approximate version of the 'one-loop dressed' integral equation, and its numerical impact turns out to be rather considerable. The detailed numerical analysis of the resulting gap equation reveals that the constituent quark mass obtained is about 300 MeV, while fermions in the adjoint representation acquire a mass in the range of (750-962) MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies

This work presents an efficient data-driven method to construct probabilistic voltage envelopes (PVE) using power flow learning in grids with network contingencies. First, a network-aware Gaussian process (GP) termed Vertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimate voltage–power functions for a few network configurations. The paper introduces a novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learned VDK-GPs to determine power flows for unseen networks, with a significant reduction in the computational complexity and hyperparameter requirements compared to alternate approaches. Simulations on the IEEE 30-Bus network demonstrate the retention and transfer of power flow knowledge in both N-1 and N-2 contingency scenarios. The MT-VDK-GP approach achieves over 50 % reduction in mean prediction error for novel N-1 contingency network configurations in low training data regimes (50–250 samples) over VDK-GP. Additionally, MT-VDK-GP outperforms a hyper-parameter based transfer learning approach in over 75 % of N-2 contingency network structures, even without historical N-2 outage data. Furthermore, the proposed method demonstrates the ability to achieve PVEs using sixteen times fewer power flow solutions compared to Monte-Carlo sampling-based methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Nonlocal effect on the fluctuation conductivity of granular superconductors

The theory of fluctuation conductivity for small impurity concentration is developed. We consider all fluctuation corrections of the first order in the case of dilute impurity concentration including nonlocal electron scattering in the clean superconductor. By using Green's function technique we first calculate the Cooperon (impurity vertex) C({rvec q},{omega}{sub 1},{omega}{sub 2}) and fluctuation propagator K({Omega}{sub k}, q) in the presence of impurities. We show that in the clean limit the density-of-states quantum corrections are canceled by the Maki-Thompson (MT) term and it results in the reduction of the total fluctuation correction in clean case to the Aslamazov-Larkin (AL) term only.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electric field enhancement in a self-assembled 2D array of silver nanospheres

We investigate the plasmonic properties of a self-assembled 2D array of Ag nanospheres (average particle diameter/inter-particle separation distance of 9/3.7 nm). The structures of the individual particles and their assemblies are characterized using high-resolution transmission electron microscopy (HR-TEM). The plasmonic response of the nanoparticle network is probed using two-photon photoemission electron microscopy (TP-PEEM). HR-TEM and TP-PEEM statistics reveal the structure and plasmonic response of the network to be homogeneous on average. This translates into a relatively uniform surface-enhanced Raman scattering (SERS) response from biphenyl,4-4{sup ′}-dithiol (BPDT) molecules adsorbed onto different sites of the network. Reproducible, bright, and low-background SERS spectra are recorded and assigned on the basis of density functional theory calculations in which BPDT is chemisorbed onto the vertex of a finite tetrahedral Ag cluster consisting of 20 Ag atoms. A notable agreement between experiment and theory allows us to rigorously account for the observable vibrational states of BPDT in the ∼200–2200 cm{sup −1} region of the spectrum. Finite difference time domain simulations further reveal that physical enhancement factors on the order of 10{sup 6} are attainable at the nanogaps formed between the silver nanospheres in the 2D array. Combined with modest chemical enhancement factors, this study paves the way for reproducible single molecule signals from an easily self-assembled SERS substrate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distinguishing Quarks and Gluons in Pion and Kaon PDFs

The leading-twist parton distribution functions of the pion and kwon are calculated for the first time using a rainbow-ladder truncation of QCD's Dyson-Schwinger equations (DSEs) that self-consistently sums all planar diagrams. The nonperturbative gluon dressing of the quarks is thereby correctly accounted for, which in practice means solving the inhomogeneous Bethe-Salpeter equation (BSE) for the quark operator that defines the spin-independent quark distribution functions. An immediate consequence of using this dressed vertex is that gluons carry 35% of the pion's and 30% of the kaon's light-cone momentum, with the remaining momentum carried by the quarks. The scale associated with these DSE results is μ 0 = 0.78 GeV. The gluon effects generated by the inhomogeneous BSE are inherently nonperturbative and cannot be mimicked by the perturbative QCD evolution equations. A key consequence of this gluon dressing is that the valence quarks have reduced support at low-to-intermediate x, where the gluons dominate, and increased support at large x. As a result, our DSE calculation of the pion's valence quark distribution is in excellent agreement with the Conway et al. pion-induced Drell-Yan data, but nevertheless exhibits the q π (x) similar or equal to (1 - x) 2 behavior as x -> 1 predicted by perturbative QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Commuting projections on graphs

For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ 2 -projection Q H onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π H from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π H and Q H commute with the discrete divergence operator, i.e., we have div π H = Q H div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.

97 MATHEMATICS AND COMPUTING↗

3-Manifolds and VOA Characters

Abstract By studying the properties ofq-series$$\widehat{Z}$$ Z ^ -invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for$$\widehat{Z}$$ Z ^ -invariants leads to many infinite families of new fermionic formulae for VOA characters.

Physics↗

The implementation of Global Feature EXtractor (gFEX) - the ATLAS Calorimeter Level 1 Trigger system for LHC Run-3 upgrade

As part of the ATLAS Phase-I Upgrade, the global Feature EXtractor (gFEX) is one of several hardware modules designed to help maintain the ATLAS Level-1 trigger acceptance rate with the increasing Large Hadron Collider (LHC) luminosity and the increasing Pile-Up conditions. The gFEX is used to identify patterns of energy associated with the hadronic decays of high momentum Higgs, W & Z bosons, top quarks, and exotic particles in real time at the 40 MHz LHC bunch crossing rate. The board is required to receive coarse-granularity (Δη×Δphiv = 0.2×0.2 gTower) information from the entire ATLAS calorimeters on 276 optical fibers. A prototype v1 with one Xilinx ZYNQ FPGA, and one Vertex-7 FPGA for technology validation has been designed and tested in 2015. With the lessons learned from the prototype v1, a prototype v2 with three Vertex UltraScale FPGAs and one ZYNQ FPGA has been implemented to verify full functionalities of gFEX in 2016. Based on the prototype v2 design, a prototype v3, the final gFEX prototype, is implemented, which is an ATCA module consisting of three Vertex UltraScale+ FPGAs, one ZYNQ UltraScale+ SoC, and 35 MiniPODs. This board receives up to 300 fiber optical links from calorimeters and transmits trigger data on 96 links to the to the ATLAS Level-1 Topological trigger (L1Topo [1]) at the speed up to 12.8 Gb/s. There are also 24 electrical links on board for communication between two FPGAs with the speed up to 25.6 Gb/s. The performance of three prototype boards have been tested and evaluated. For the prototype v3 board, the high-speed optical links are stable at 12.8 Gb/s with Bit Error Ratio (BER) < 1 × 10 -15 . The low-latency parallel GPIO (General Purpose I/O) buses between FPGAs are stable at 1.12 Gb/s. The peripheral components of ZYNQ UltraScale+ SoC, such as 16 GB DDR4 DIMM, UART, SPI flashes, and Ethernet, have also been verified. Here, the test results of the prototype v3 board validate the gFEX technologies, architecture and full functionalities. Now the final production board is being produced.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On D-brane -anti D-brane effective actions and their all order bulk singularity structures

All four point functions of brane anti brane system including their correct all order α{sup ′} corrections have been addressed. All five point functions of one closed string Ramond-Ramond (RR), two real tachyons and either one gauge field or the scalar field in both symmetric and asymmetric pictures have also been explored. The entire analysis of is carried out. Not only does it fix the vertex operator of RR in asymmetric picture and in higher point functions of string theory amplitudes but also it confirms the fact that there is no issue of picture dependence of the mixed closed RR, gauge fields, tachyons and fermion fields in all symmetric or anti symmetric ones. We compute S-matrix in the presence of a transverse scalar field, two real tachyons and that reveals two different kinds of bulk singularity structures, involving an infinite number of u-channel gauge field and (u+s{sup ′}+t{sup ′})-channel scalar bulk poles. In order to produce all those bulk singularity structures, we define various couplings at the level of the effective field theory that involve the mixing term of Chern-Simons coupling (with C-potential field) and a covariant derivative of the scalar field that comes from the pull-back of brane. Eventually we explore their all order α{sup ′} corrections in the presence of brane anti brane system where various remarks will be also pointed out.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A note on the S-matrix bootstrap for the 2d O(N) bosonic model

In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O ( N ) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model. Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints. Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex. This is a standard problem in applied mathematics, related to semi-definite programming and solvable by fast available numerical algorithms. The information provided by the numerical solution is enough to reproduce the known analytical solution without using integrability, namely the Yang-Baxter equation. This situation seems quite generic so we expect that other theories without continuous parameters can also be found by maximizing linear functionals in the convex space of allowed S-matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SLICING AND DICING THE MILKY WAY DISK IN THE SLOAN DIGITAL SKY SURVEY

We use the Stripe 82 proper-motion catalog of Bramich et al. to study the kinematics of Galactic disk stars in the solar neighborhood. We select samples of dwarf stars with reliable spectra and proper motions. They have cylindrical polar radii between 7 {<=} R {<=} 9 kpc, heights from the Galactic plane satisfying |z| {<=} 2 kpc, and span a range of metallicities -1.5 {<=} [Fe/H] {<=} 0. We develop a method for calculating and correcting for the halo contamination in our sample using the distribution of rotational velocities. Two Gaussians representing disk and halo populations are used to fit the radial (v{sub R} ) and vertical (v{sub z} ) velocity distributions via maximum likelihood methods. For the azimuthal velocities (v{sub {phi}}) the same technique is used, except that a skewed non-Gaussian functional form now represents the disk velocity distribution. This enables us to compute the dispersions {sigma}{sub R}, {sigma}{sub z}, {sigma}{sub {phi}}, and cross-terms (the tilt {sigma}{sub Rz} and the vertex deviation {sigma}{sub R{phi}}) of the velocity ellipsoid as a function of height and metallicity. We also investigate the rotation lag of the disk, finding that the more metal-poor stars rotate significantly slower than the metal-rich stars. These samples provide important constraints on heating mechanisms in the Galactic disk and can be used for a variety of applications. We present one such application employing the Jeans equations to provide a simple model of the potential close to the disk. Our model is in excellent agreement with others in the literature and provides an indication that the disk, rather than the halo, dominates the circular speed at the solar neighborhood. We obtain a surface mass density within 1.1 kpc of around 66 M{sub Sun} pc{sup -2} and estimate a local halo density of 0.015 M{sub Sun} pc{sup -3} = 0.57 GeV cm{sup -3}.

79 ASTRONOMY AND ASTROPHYSICS↗

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

It is generally believed that in a two-dimensional metal, whose ground state is antiferromagnetically ordered with Q = (π,π), thermal (static) magnetic fluctuations give rise to precursor behavior above TN in which the spectral function of a hot fermion (the one for which k and k + Q are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of T > T N and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, such as, e.g., Eliashberg theory for magnetically mediated superconductivity. We also analyze the potential pseudogap behavior at T = 0. Here, we argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Reciprocal Control of Hierarchical DNA Origami-Nanoparticle Assemblies

DNA origami mechanisms offer promising tools for precision nanomanipulation of molecules or nanomaterials. Recent advances have extended the function of individual DNA origami devices to material scales via hierarchical assemblies. However, achieving rapid and precise control of large conformational changes in hierarchical assemblies remains a critical challenge. In this work, we demonstrate a method for controlling DNA origami-nanoparticle assemblies through a multiscale approach, in which nanoparticles impart control on the conformation of individual DNA origami mechanisms, whereas DNA origami assemblies control the conformation of nanoparticle arrays. Specifically, we show that the angular distributions of DNA origami hinge mechanisms are tunable as a function of nanoparticle size and distance from the hinge vertex. We selectively adjust the affinity of nanoparticle binding sites, resulting in hinge actuation via DNA melting without releasing the nanoparticle, thereby enabling rapid and reversible temperature-based actuation. Finally, we demonstrate this rapid actuation in DNA origami-nanoparticle arrays of length scales extending over a micron. These results provide guiding principles toward the design of dynamic, DNA-origami hierarchical materials capable of storing and releasing mechanical energy.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Higgs oscillations in time-resolved optical conductivity

Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Nonequilibrium superconductors are often studied using time-resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven nonequilibrium state requires careful attention in the time domain. We calculate the time-resolved optical conductivity of a pumped superconducting state using a nonequilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full vertex corrections and used to characterize the transient superconducting state. The transient optical conductivity shows the suppression of the superconducting order parameter in the time domain. The subsequent recovery of the order parameter exhibits oscillatory behavior that corresponds to the Higgs amplitude mode, and may be seen in several parts of the spectrum.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tensor network implementation of bulk entanglement spectrum

Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in T. Hsieh and L. Fu (arXiv:1305.1949). This involved computing the bulk entanglement spectrum (BES) of the ground state upon tracing out an extensive subsystem. Here, this work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d +1 dimensions, which can be studied using Monte Carlo or tensor renormalization-group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the Affleck-Kennedy-Lieb-Tasaki (AKLT) wave function (and its generalizations) remarkably contains critical six-vertex (and, in general, eight-vertex) models within it.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Real-space observation of ergodicity transitions in artificial spin ice

Abstract Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NLO vertex for a forward jet plus a rapidity gap at high energies

We present the calculation of the forward jet vertex associated to a rapidity gap (coupling of a hard pomeron to the jet) in the BFKL formalism at next-to-leading order (NLO). Real emission contributions are computed via Lipatov’s effective action. The NLO jet vertex turns out to be finite within collinear factorization and allows, together with the NLO non-forward gluon Green’s function, to perform NLO studies of jet production in diffractive events (e.g. Mueller-Tang dijets)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗