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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Casimir recursion relations for general conformal blocks

We study the structure of series expansions of general spinning conformal blocks. We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in Gelfand-Tsetlin basis, of which the Gegenbauer polynomials are a special case. We study the properties of these functions and explain how they can be computed in practice. We show how the Casimir equation in Dolan-Osborn coordinates leads to a simple one-step recursion relation for the coefficients of the series expansion of general spinning conformal block. The form of this recursion relation is determined by 6j symbols of Spin(d – 1). In particular, it can be written down in closed form in d = 3, d = 4, for seed blocks in general dimensions, or in any other situation when the required 6j symbols can be computed. As a result, we work out several explicit examples and briefly discuss how our recursion relation can be used for efficient numerical computation of general conformal blocks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

On triality defects in 2d CFT

We consider the triality fusion category discovered in the c = 1 Kosterlitz-Thouless theory. We analyze this fusion category using the tools from the group theoretical fusion category and compute the simple lines, fusion rules and F-symbols. We then studied the physical implication of this fusion category including deriving the spin selection rule, computing the asymptotic density of states of irreducible representations of the fusion category symmetries, and analyzing its anomaly and constraints under the renormalization group flow. There is another set of F-symbols for the fusion categories with the same fusion rule known in the literature. We find these two solutions are different as they lead to different spin selection rules. This gives a complete list of the fusion categories with the same fusion rule by the classification result in.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Landau singularities and symbology: One- and two-loop MHV amplitudes in SYM theory

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Non-perturbative geometries for planar $ \mathcal{N} $ = 4 SYM amplitudes

There is a remarkable well-known connection between the G(4, n) cluster algebra and n-particle amplitudes in $ \mathcal{N} $ = 4 SYM theory. For n ≥ 8 two long-standing open questions have been to find a mathematically natural way to identify a finite list of amplitude symbol letters from among the infinitely many cluster variables, and to find an explanation for certain algebraic functions, such as the square roots of four-mass-box type, that are expected to appear in symbols but are not cluster variables. In this letter we use the notion of “stringy canonical forms” to construct polytopal realizations of certain compactifications of (the positive part of) the configuration space Conf n (P k–1 ) ≅ G(k, n)/T that are manifestly finite for all k and n. Some facets of these polytopes are naturally associated to cluster variables, while others are naturally associated to algebraic functions constructed from Lusztig’s canonical basis. For (k, n) = (4, 8) the latter include precisely the expected square roots, revealing them to be related to certain “overpositive” functions of the kinematical invariants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

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↗
DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗
DOE OSTI2021

Algebraic branch points at all loop orders from positive kinematics and wall crossing

A bstract There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $$ \mathcal{N} $$ N = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Landau singularities of the 7-point ziggurat. Part I

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point “ziggurat” graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the “heptagon symbol alphabet” that has appeared in the context of planar Ν = 4 super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Cluster bootstrap for cosmological correlators

We show that cosmological wavefunction coefficients associated with n-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of A 2n−2 and B 2n−1 cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph “tubings” that appear in the kinematic flow equation and polygon “triangulations” that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the ϵ expansion around the de Sitter limit. We use this information as bootstrap input to show that de Sitter symbols for n ≤ 4 are uniquely determined by simple physical constraints.

differential and algebraic geometry↗
DOE OSTI2018

Well-Posedness and Spectral Analysis of Integrodifferential Equations Arising in Viscoelasticity Theory

We study the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces and provide a spectral analysis of operator functions that are symbols of the specified equations. These equations represent an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory and other important applications. For the said integrodifferential equations, we obtain well-posedness results in weighted Sobolev spaces of vector functions defined on the positive semiaxis and valued in a Hilbert space. For the symbols of the said equations, we find the localization and the structure of the spectrum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Atomic Theory of Division and Intersection of Semiring Ideals

We consider two-sided ideals of semirings. More precisely, we study the theory of two-sided ideals in the signature consisting of the predicate symbol ⊆ and three function symbols that denote the intersection, right division, and left division of ideals. We prove the decidability of the set of those atomic formulas in this signature that are valid for all semirings and all valuations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗
DOE OSTI2019

Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method

This paper secures new nematicons in liquid crystals from its governing equation by extended sinh-Gordon equation expansion method with the aid of symbolic computational package Maple. The two laws of nonlinearity, namely Kerr and parabolic laws are studied. As outcomes, some new explicit complex hyperbolic and complex trigonometric function solutions are derived regarding dark, bright, combined dark–bright, singular, combined singular optical, periodic wave, dipole soliton solutions and others. To show the real physical meaning of the derived results, three dimensional graphs with contours and two dimensional graphs are prepared under the choice of proper values of the arbitrary parameters. The derived solutions have been checked back into their corresponding equations with the symbolic computational package Maple. All the combined solutions are found to be new, which may play an important role in the context of liquid crystals. The applied method is found to provide a powerful tool for extracting exact solitary wave solutions and overcome the difficulties of the solitary wave ansatz method.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Homogenizing atomic dynamics by fractional differential equations

In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches. - Highlights: • Match the dispersion relation of linear chain by power function of fractional order, added on low order Taylor expansion. • Design FDE by approximating dispersion relation, or the symbol for the force term. • Solve the FDE by algorithm of spectral accuracy. • Obtain faithful and systematical homogenization when resolved at coarser grid. • Applies to general lattices: complex, nonlinear and multidimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Ternary rare-earth zinc arsenides REZn{sub 1-x}As{sub 2} (RE=La-Nd, Sm)

The ternary rare-earth zinc arsenides REZn{sub 1-x}As{sub 2} (RE=La-Nd, Sm) were prepared by reaction of the elements at 800 deg. C. Single-crystal and powder X-ray diffraction analysis revealed a defect SrZnBi{sub 2}-type average structure for the La member (Pearson symbol tI16, space group I4/mmm, Z=4; a=4.0770(9) A, c=20.533(5) A), in contrast to defect HfCuSi{sub 2}-type average structures for the remaining RE members (Pearson symbol tP8, space group P4/nmm, Z=2; a=4.0298(5)-3.9520(4) A, c=10.222(1)-10.099(1) A in the progression from Ce to Sm). The homogeneity range is not appreciable (estimated to be narrower than 0.6<1-x<0.7 in SmZn{sub 1-x}As{sub 2}) and the formula REZn{sub 0.67}As{sub 2} likely represents the Zn-rich phase boundary. The Ce-Nd members are Curie-Weiss paramagnets. LaZn{sub 0.67}As{sub 2} shows activated behavior in its electrical resistivity, whereas SmZn{sub 0.67}As{sub 2} exhibits anomalies in its temperature dependence of the electrical resistivity. - Graphical abstract: LaZn{sub 1-x}As{sub 2} adopts a SrZnBi{sub 2}-type structure whereas the remaining members of the REZn{sub 1-x}As{sub 2} series (RE=Ce-Nd, Sm) adopt a HfCuSi{sub 2}-type structure. Highlights: > REZn{sub 1-x}As{sub 2} adopts SrZnBi{sub 2}-type (RE=La) or HfCuSi{sub 2}-type (RE=Ce-Nd, Sm) structures. > Trends in RE substitution and local distortion around Zn-centered tetrahedra can be rationalized by geometrical factors. > Zn vacancies occur to reduce Zn-As and As-As antibonding interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Crystal structures, fluorescent and magnetic properties of five new coordination polymers based on biphenyl-3,4 Prime ,5-tricarboxylic acid

Five new coordination polymers, {l_brace}[Cd{sub 3}(bpt){sub 2}(DMF){sub 2}]{center_dot}(H{sub 2}O){sub 2}{r_brace}{sub n} (1), [Cd(Hbpt)(bipy){sub 0.5}(H{sub 2}O)]{sub n} (2), [Cd{sub 2}(bpt)(phen){sub 2}Cl]{sub n} (3), {l_brace}[Cu{sub 2}(bpt)(phen)({mu}{sub 2}-OH)(H{sub 2}O)]{center_dot}(H{sub 2}O){sub 2}{r_brace}{sub n} (4) and {l_brace}[Mn{sub 5}(Hbpt){sub 4}(phen){sub 4}({mu}{sub 2}-OH){sub 2}(H{sub 2}O){sub 2}]{center_dot}(H{sub 2}O){sub 2}(CH{sub 3}CN){sub 2}{r_brace}{sub n} (5) have been prepared through hydro(solvo)thermal reactions of H{sub 3}bpt (H{sub 3}bpt=biphenyl-3,4 Prime ,5-tricarboxylic acid) with different pyridyl-containing auxiliary ligands (bipy=4,4 Prime -bipyridine and phen=1,10-phenanthroline). Compound 1 represents a 3D ladder-like framework composed of rod-shaped infinite chains. In 2, the bridging ligand bipy links binuclear cadmium ions to generate a 2D layer. Compound 3 features a 1D ladder structure and further linked by {pi}-{pi} stacking interaction to form a 3D supramolecular network. Compound 4 exhibits a binodal 3-connected net which features the Schlafli symbol of (4{center_dot}8{sup 2}). Compound 5 contains trimetallic cluster and binuclear unite which are further linked by Hbpt ligand to form a 2D layer. Moreover, photoluminescent properties of compounds 1-3 were studied in the solid state. Magnetic susceptibility measurements indicate that compound 4 exhibits ferromagnetic exchange interactions, whereas compound 5 displays antiferromagnetic exchange interactions. - Graphical abstract: Five new coordination polymers have been prepared through reactions of H{sub 3}bpt with different pyridyl-containing auxiliary ligands. The bpt exhibits four new kinds of coordination modes with 'V or Y shape'. Highlights: Black-Right-Pointing-Pointer 1 represents a unique (4{center_dot}8)-connected network with a Schlafli symbol (4{sup 6})(4{sup 12}{center_dot}6{sup 12}{center_dot}8{sup 4}). Black-Right-Pointing-Pointer Compound 4 shows ferromagnetic interaction between the dimeric Cu{sup 2+} units. Black-Right-Pointing-Pointer The bpt ligand exhibits four new kinds of coordination modes with 'V or Y shape'.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Synthesis, crystal structures and properties of lanthanide-organic frameworks based benzene carboxylates with two/three-dimensional structure

A series of lanthanide coordination polymers, {l_brace}[Dy{sub 3}(1,3-BDC){sub 4}(NO{sub 3})(phen){sub 3}]{center_dot}2H{sub 2}O{r_brace}{sub n} (1), {l_brace}[Dy{sub 2}(1,3-BDC){sub 3}(H{sub 2}O){sub 2}]{center_dot}H{sub 2}O{r_brace}{sub n} (2), {l_brace}[Ln{sub 4}(1,3-BDC){sub 6}(DMF)(H{sub 2}O){sub 4}]{center_dot}DMF{center_dot}2H{sub 2}O{r_brace}{sub n} (Ln=Tb (3), Ho (4), Er (5), 1,3-H{sub 2}BDC=1,3-benzenedicarboxylate, phen=1,10-phenanthroline, DMF=N,N-dimethylformamide), have been synthesized and characterized. In coordination polymer 1, each Dy{sup 3+} ion is connected to its neighboring Dy{sup 3+} ion through bridging carboxyl oxygen atoms of the 1,3-BDC{sup 2-} ligands to form a new three-dimensional open-framework structure which the Schlaefli symbol of {l_brace}6{sup 4}{center_dot}8{sup 2}{r_brace}{sub 2}{l_brace}6{sup 6}{r_brace}. In coordination polymer 2, center metal dysprosium ions are interlaced and connected through bridging carboxyl oxygen atoms to form an infinite helix chain. Two helix chains are linked through the 1,3-BDC{sup 2-} ligand to give rise to the two-dimensional layered structure. Coordination polymers 3-5 are isomorphous, which displays a (3,4)-connected net with the point symbol of {l_brace}4{sup 2}{center_dot}6{sup 3}{center_dot}8{r_brace}{l_brace}4{sup 2}{center_dot}6{r_brace}. The solid-state photoluminescence properties and lifetimes of the Dy (1 and 2) and Tb (3) coordination polymers have been measured at room temperature. Highlights: Black-Right-Pointing-Pointer Five lanthanide coordination polymers based on 1,3-H{sub 2}BDC were obtained. Black-Right-Pointing-Pointer The polymers were structurally characterized by single-crystal X-ray diffraction. Black-Right-Pointing-Pointer Coordination polymers 1-5 display different topological structures. Black-Right-Pointing-Pointer They show characteristic emissions of lanthanide ions in the solid state.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Construction of two novel indium phosphites with (3,6)- and (3,5)-connected frameworks: Synthesis, structure and characterization

Two novel anionic indium phosphites, formulated as [H{sub 3}O][In(HPO{sub 3}){sub 2}] (1) and [C{sub 4}H{sub 12}N{sub 2}][In{sub 2}(HPO{sub 3}){sub 3}(C{sub 2}O{sub 4})] (2), were prepared under hydrothermal conditions by using piperazine (PIP) as a structure-directing agent (SDA). Single-crystal X-ray diffraction analysis reveals that compounds 1 and 2 crystallize in the hexagonal space group P6{sub 3}mc (No. 186) and orthorhombic space group Cmcm (No. 63), respectively. Compound 1, constructed from InO{sub 6} octahedra and HPO{sub 3} pseudo-pyramids, exhibits a rare (3,6)-connected layer structure with kgd (Kagome dual) topology. Compound 2, on the other hand, features a 3D phosphite-oxalate hybrid structure with intersecting 8- and 12-MRs channels. From a topological perspective 2 can be regarded as a (3, 5)-connected binodal net with the Schlaefli symbol (4{sup 2}.6)(4{sup 2}.6{sup 5}.8{sup 3}). Highlights: Black-Right-Pointing-Pointer Two novel indium phosphite and indium phosphite-oxalate hybrid compounds are synthesized. Black-Right-Pointing-Pointer (3, 6)-connected layer structure with kgd topology. Black-Right-Pointing-Pointer (3,5)-connected binodal net with the Schlaefli symbol (4{sup 2}.6)(4{sup 2}.6{sup 5}.8{sup 3}).

36 MATERIALS SCIENCE↗