Monopole and quadrupole contributions to the angular momentum density
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Results for “Tensor factorizations”
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Collinear limit of the four-point energy correlator in N = 4 supersymmetric Yang-Mills theory
We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are collinear. This formula is derived by combining a simplified, manifestly dual conformal invariant form of the 1 → 4 splitting function obtained from the square of the tree-level five-particle form factor of stress-tensor multiplet operators, with a novel integration-by-parts algorithm operating directly on Feynman parameter integrals. Our results provide valuable data for exploring the structure of physical observables in perturbation theory, and for calculations of jet substructure observables in quantum chromodynamics. Published by the American Physical Society 2024
Chicherin, Dmitry (ORCID:000000028985084X)↗
Singularities of Generalized Parton Distributions
The basic ideas of the theory of Generalized Parton Distributions (GPDs) are reviewed. Recent developments in the study of singularities of GPDs are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum stress and torsion distributions in the deuteron
Stress distributions in the deuteron are related to form factors of the asymmetric energy-momentum tensor through three-dimensional Fourier transforms. There are eleven such form factors, which we calculate in an impulse approximation. We compare the obtained form factors to prior results for the six form factors that have been previously calculated. We then elaborate on the formalism for relating the form factors to internal distributions of mass, mass flux, momentum, stresses, and forces, and obtain results for all of these distributions. We obtain the principal stresses for the symmetric part of the stress tensor, and show that the antisymmetric part describes the reorientation of fermion spin by torsion stress when the nucleon moves between the S and D waves. Force distributions in the nucleons depend on the so-called nonconserved form factors through the Cauchy momentum equation, and are nonradial owing to the presence of tensor forces and spin-orbit coupling.
QCD phenomenology↗
The three-point form factor of Tr ϕ 3 to six loops
We study the three-point form factor of the length-three half-BPS operator (Tr ϕ 3 ) in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ 2 ). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Recurrent features of amplitudes in planar $\mathcal{N}$ = 4 super Yang-Mills theory
The planar three-gluon form factor for the chiral stress tensor operator in planar maximally supersymmetric Yang-Mills theory is an analog of the Higgs-to-three-gluon scattering amplitude in QCD. The amplitude (symbol) bootstrap program has provided a wealth of high-loop perturbative data about this form factor, with results up to eight loops available. The symbol of the form factor at L loops is given by words of length 2L in six letters with associated integer coefficients. In this paper, we analyze this data, describing patterns of zero coefficients and relations between coefficients. We find many sequences of words whose coefficients are given by closed-form expressions which we expect to be valid at any loop order. Moreover, motivated by our previous machine-learning analysis, we identify simple recursion relations that relate the coefficient of a word to the coefficients of particular lower-loop words. These results open an exciting door for understanding scattering amplitudes at all loop orders.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Effects of domain, grain, and magnetic anisotropy distributions on magnetic permeability: Monte-Carlo approach
Existing approaches for prediction of the tensor permeability of polycrystalline ferrites may not provide reasonable estimates of demagnetized permeability below the spin resonance (i.e., low-field loss region) or in cases of partial magnetization. We propose an approach which solves the coupled Landau-Lifshitz-Gilbert equation for the dynamic magnetic fields including the minimization of free energy to determine the equilibrium magnetization direction. Unlike previous models, we employ a Monte-Carlo approach to easily calculate the (ensemble) averages of permeability over various domain/grain structures and magnetic anisotropy conditions. Material differences, such as those resulting from different preparation methods, are expressed by using probability density functions (p.d.f.) for anisotropy angle (easy axis angle), grain demagnetization factor (ng), and domain demagnetization factor (nd). Effects on the permeability tensor of grain and domain demagnetization factors and anisotropy field relative to saturation magnetization are discussed for the partially magnetized states for polycrystalline ferrites. It is found that the grain structure (i.e., grain demagnetization distribution) has a smaller effect on the frequency dependent permeability than does the same distribution of domains (i.e., domain demagnetization distribution).
36 MATERIALS SCIENCE↗
Transmural Remodeling of Cardiac Microstructure in Aged Spontaneously Hypertensive Rats by Diffusion Tensor MRI
The long-standing high blood pressure (also known as hypertension) overworks the heart. Microstructural remodeling is a key factor of hypertensive heart disease progression. Diffusion tensor magnetic resonance imaging (DT-MRI) is a powerful tool for the rapid noninvasive nondestructive delineation of the cardiomyocyte organization. The spontaneously hypertensive rat (SHR) is a well-established model of genetic hypertension. The goal of this study was to employ high-resolution DT-MRI and the SHR animal model to assess the transmural layer-specific remodeling of myocardial microstructure associated with hypertension. Ex vivo experiments were performed on excised formalin-fixed hearts of aged SHRs (n = 4) and age-matched controls (n = 4). The DT-MRI-derived fractional anisotropy (FA), longitudinal diffusivity (λ L ), transversal diffusivity (λ T ), and mean diffusivity (MD) served as the readout parameters investigated at three transmural zones (i.e., endocardium, mesocardium, and epicardium). The helix angles (HAs) of the aggregated cardiomyocytes and the orientation of laminar sheetlets were also studied. Compared with controls, the SHRs exhibited decreased epicardial FA, while FA changes in the other two transmural regions were insignificant. No substantial differences were observed in the diffusivity parameters and the transmural course of HAs between the two groups. A consistent distribution pattern of laminar sheetlet orientation was not identified for either group. Our findings are in line with the known cellular microstructure from early painstaking histological studies. Biophysical explanations of the study outcomes are provided. In conclusion, our experimental findings indicate that the epicardial microstructure is more vulnerable to high blood pressure leading to more pronounced changes in this region during remodeling. DT-MRI is well-suited for elucidating these alterations. The revealed transmural nonuniformity of myocardial reorganization may shed light on the mechanisms of the microstructure-function relationship in hypertension progression. Our results provide insights into the management of patients with systemic arterial hypertension, thus prevent the progression toward heart failure. The findings of this study should be acknowledged by electromechanical models of the heart that simulate the specific cardiac pathology.
60 APPLIED LIFE SCIENCES↗
Phenomenology of $ {\Lambda}_b\to {\Lambda}_c\tau {\overline{\nu}}_{\tau } $ using lattice QCD calculations
In a recent paper we studied the effect of new-physics operators with different Lorentz structures on the semileptonic Λ<!-- Λ --> b →<!-- → --> Λ<!-- Λ --> c τ<!-- τ --> ν<!-- ν --> ¯<!-- ¯ --> τ<!-- τ --> decay. This decay is of interest in light of the R(D (*)) puzzle in the semileptonic B ¯<!-- ¯ --> →<!-- → --> D ( ∗<!-- * --> ) τ<!-- τ --> ν<!-- ν --> ¯<!-- ¯ --> τ<!-- τ --> decays. In this work we add tensor operators to extend our previous results and consider both model-independent new physics (NP) and specific classes of models proposed to address the R(D (*)) puzzle. We show that a measurement of R ( Λ<!-- Λ --> c ) = B [ Λ<!-- Λ --> b →<!-- → --> Λ<!-- Λ --> c τ<!-- τ --> ν<!-- ν --> ¯<!-- ¯ --> τ<!-- τ --> ] / B [ Λ<!-- Λ --> b →<!-- → --> Λ<!-- Λ --> c ℓ<!-- ℓ --> ν<!-- ν --> ¯<!-- ¯ --> ℓ<!-- ℓ --> ] can strongly constrain the NP parameters of models discussed for the R(D (*)) puzzle. We use form factors from lattice QCD to calculate all Λ<!-- Λ --> b →<!-- → --> Λ<!-- Λ --> c τ<!-- τ --> ν<!-- ν --> ¯<!-- ¯ --> τ<!-- τ --> observables. The Λ b → Λ c tensor form factors had not previously been determined in lattice QCD, and we present new lattice results for these form factors here.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
EQUATION OF STATE FOR MASSIVE NEUTRON STARS
Using the relativistic Hartree-Fock approximation, we investigate the properties of neutron-star matter in detail. In the present calculation, we consider not only the tensor coupling of vector mesons to octet baryons and the form factors at interaction vertices but also the change in the internal (quark) structure of baryons in dense matter. The relativistic Hartree-Fock calculations are performed in two ways: one with coupling constants determined by SU(6) (quark model) symmetry and the other with coupling constants based on SU(3) (flavor) symmetry. For the latter case, we use the latest Nijmegen (ESC08) model. Then, it is very remarkable that the particle composition of the core matter in SU(3) symmetry is completely different from that in SU(6) symmetry. In SU(6) symmetry, all octet baryons appear in the density region below {approx}1.2 fm{sup -3}, while in the ESC08 model only the {Xi}{sup -} hyperon is produced. Furthermore, the medium modification of the internal baryon structure hardens the equation of state for the core matter. Taking all these effects into account, we can obtain the maximum neutron-star mass which is consistent with the recently observed mass, 1.97 {+-} 0.04 M{sub Sun} (PSR J1614-2230). We therefore conclude that the extension from SU(6) symmetry to SU(3) symmetry in meson-baryon couplings and the internal baryon structure variation in matter considerably enhance the mass of neutron stars. Furthermore, the effects of the form factor at the vertex and the Fock contribution, including the tensor coupling due to vector mesons, are indispensable for describing the core matter.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Exploration of Electrochemical Reactions at Organic–Inorganic Halide Perovskite Interfaces via Machine Learning in In Situ Time-of-Flight Secondary Ion Mass Spectrometry
The instability of hybrid organic–inorganic perovskite (HOIP) devices is one of the significant challenges preventing commercialization. Exploring these phenomena is severely limited by the complexity of the intrinsic electrochemistry of HOIPs, the presence of multiple volatile and mobile ionic species, and the possible role of environmentally induced reactions at surfaces and triple-phase junctions. Here, in situ studies of the electrochemistry of methylammonium lead bromide perovskite with the Au electrode interface are reported via light- and voltage-dependent time-of-flight secondary ion mass spectrometry (ToF-SIMS) imaging of lateral perovskite heterostructures. While ToF-SIMS allows for the visualization of the chemical composition along the surface and its evolution with light and electrical bias, the interpretation of the multidimensional data obtained is often limited due to strong correlations between chemical signatures and the need to track multiple peaks at once. Here, a machine learning workflow combining the Hough transform and non-negative matrix factorization and no-negative tensor decomposition is developed to avoid this limitation and extract salient features of associated chemical changes and to separate the light- and voltage-dependent dynamics. Finally, combining these in situ characterizations and the machine learning workflow provides comprehensive information on the chemical nature of moving species, ion accumulation, and interfacial electrochemical reactions in HOIP devices.
36 MATERIALS SCIENCE↗
The gravitational form factors of the electron in quantum electrodynamics
Not Available
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
spdlayers
Symmetric Positive Definite (SPD) enforcement layers for PyTorch. Regardless of the input, the output of these layers will always be a SPD tensor! The `Cholesky` layer uses a cholesky factorization to enforce SPD, and the `Eigen` layer uses an eigendecomposition to enforce SPD. Both layers take in some tensor of shape `[batch_size, input_shape]` and output a SPD tensor of shape`[batch_size, output_shape, output_shape]`. The relationship between input and output is defined by the following. ```python input_shape = sum([i for i in range(output_shape + 1)]) ``` The layers have no learnable parameters, and merely serve to transform a vector space to a SPD matrix space.
Jekel, CharlesF.↗
Parallel Nonnegative CP Decomposition of Dense Tensors
The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensors that can enforce nonnegativity of the computed low-rank factors. The principal task is to parallelize the Matricized-Tensor Times Khatri-Rao Product (MTTKRP) bottleneck subcomputation. The algorithm is computation efficient, using dimension trees to avoid redundant computation across MTTKRPs within the alternating method. Our approach is also communication efficient, using a data distribution and parallel algorithm across a multidimensional processor grid that can be tuned to minimize communication. We benchmark our software on synthetic as well as hyperspectral image and neuroscience dynamic functional connectivity data, demonstrating that our algorithm scales well to 100s of nodes (up to 4096 cores) and is faster and more general than the currently available parallel software.
Ballard, Grey↗
Multi-Area Model-Free State Estimation via Distributed Tensor Decomposition
This paper proposes a model-free method for distribution system state estimation based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A third-order tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. To demonstrate the efficacy of the developed algorithm, numerical simulations are carried out using an IEEE test system.
alternating direction method of multipliers↗
A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.
Kielstra, P Michael↗
Visser's massive graviton bimetric theory revisited
A massive gravity theory was proposed by Visser in the late 1990s. This theory, based on a background metric b{sub {alpha}{beta}} and on an usual dynamical metric g{sub {alpha}{beta}} has the advantage of being free of ghosts as well as discontinuities present in other massive theories proposed in the past. In the present investigation, the equations of Visser's theory are revisited with particular care on the related conservation laws. It will be shown that a multiplicative factor is missing in the graviton tensor originally derived by Visser, which has no incidence on the weak field approach but becomes important in the strong field regime when, for instance, cosmological applications are considered. In this case, contrary to some previous claims found in the literature, we conclude that a nonstatic background metric is required in order to obtain a solution able to mimic the {Lambda}CDM cosmology.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗