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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1971

Radiation from a parallel-plate waveguide into a dielectric or plasma layer.

An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hilbert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.

Kostelnicek, R. J.↗
NASA NTRS1972

Penny-shaped interface crack between an elastic layer and a half space.

The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.

Erdogan, F.↗
NASA NTRS1972

A circumferential crack in a cylindrical shell under torsion.

The fully antisymmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.

Erdogan, F.↗
NASA NTRS1972

The inverse scattering problem at fixed angular momentum for nonlocal separable interactions

The problem of inverse scattering at fixed angular momentum is considered. The problem is particularized to the case of nonlocal separable interactions. A brief survey of the inverse problem for nonlocal separable interactions is presented. This problem can be solved exactly by integration. It amounts to solving singular integral equations of the Hilbert-Mushkhelishvili type, which have been studied extensively in the past and appear in many areas of physics, including theory of elasticity and dispersions relations in high energy physics.

Chadan, K.↗
NASA NTRS1973

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Erdogan, F.↗
NASA NTRS1973

Interaction between parallel cracks in layered composites

The plane strain problem of a multi-layered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.

Ratwani, M.↗
NASA NTRS1973

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Pacella, A. H.↗
NASA NTRS1973

Transverse cracks in a strip with reinforced surfaces

The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometrics and degrees of surface reinforcement.

Krenk, S.↗
NASA NTRS1974

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin Transforms the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given in the paper include the stress intensity factors, the strain energy release rates, and the probable clevage angles giving the direction of crack propagation.

Erdogan, F.↗