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Complex multiscale flows associated with instabilities and turbulence are commonly induced under high-energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. x-ray photon correlation spectroscopy (XPCS) with coherent xx-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. Our theory is validated with simulated XPCS for Brownian particles advected in multiscale flows. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS, single-pulse xx-ray speckle visibility spectroscopy (XSVS), and double-pulse XSVS. Published by the American Physical Society2025 

Abstract This article presents a novel derivation for the governing equations of geometrically curved and twisted three-dimensional Timoshenko beams. The kinematic model of the beam was derived rigorously by adopting a parametric description of the axis of the beam, using the local Frenet–Serret reference system, and introducing the constraint of the beam cross ection planarity into the classical, first-order strain versus displacement relations for Cauchy’s continua. The resulting beam kinematic model includes a multiplicative term consisting of the inverse of the Jacobian of the beam axis curve. This term is not included in classical beam formulations available in the literature; its contribution vanishes exactly for straight beams and is negligible only for curved and twisted beams with slender geometry. Furthermore, to simplify the description of complex beam geometries, the governing equations were derived with reference to a generic position of the beam axis within the beam cross section. Finally, this study pursued the numerical implementation of the curved beam formulation within the conceptual framework of isogeometric analysis, which allows the exact description of the beam geometry. This avoids stress locking issues and the corresponding convergence problems encountered when classical straight beam finite elements are used to discretize the geometry of curved and twisted beams. Finally, this article presents the solution of several numerical examples to demonstrate the accuracy and effectiveness of the proposed theoretical formulation and numerical implementation.