We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: A broad class of nonlinear classical field theories are believed to have a stationary turbulent state-a far-from-equilibrium state, even at weak coupling.
View Article and Find Full Text PDFBackground: Operative risk for supra-aortic trunk (SAT) surgical revascularization for occlusive disease, particularly transthoracic reconstruction (TR), remains ill-defined. This study sought to describe and compare 30-day outcomes of TR and extra-anatomic (ER) SAT surgical reconstruction for an occlusive indication across the United States over a contemporary 15-year period.
Methods: Using the National Surgical Quality Improvement Program, TR and ER performed during 2005-2019 were identified.
Purpose: To determine the feasibility and acceptability of using a patient decision aid (DA) for women with elevated breast cancer risk who are considering MRI screening.
Methods: This pilot study employed a mixed methods design to develop, modify, and test an interactive DA. The DA was administered among a consecutive patient sample with an estimated Tyrer-Cuzick v.