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The Goos-Hänchen and Imbert-Fedorov shifts are significant wave phenomena, yet the underlying mechanism governing the spatiotemporal vortex pulses reflected and refracted on graphene remains opaque. In this study, we analytically derive the expressions for the centroid shifts of spatiotemporal vortex pulses by applying the Fresnel-Snell formulas to each plane wave in the incident spatiotemporal vortex pulse spectrum. We demonstrate that the longitudinal shifts are correlated with the angular shifts, and thus, both are subject to resonant enhancement in the vicinity of the Brewster angle.
View Article and Find Full Text PDFScintillation restricts the development of free space optical communication in near-space hypersonic vehicles. We derived analytical formulae for the on-axis scintillation index of a partially coherent flat-topped beam in a bidirectional turbulent atmosphere and plasma link based on the Collins formula. The numerical results indicate that over long-distance propagation ranges, the on-axis scintillation index of a partially coherent flat-topped beam in bidirectional transmission is smaller than that of a Gaussian Schell model beam under the same conditions.
View Article and Find Full Text PDFIn this study, we explore the behavior of Bessel beams as they propagate through a misaligned apertured optical system in practice. Based on experimental observations, we propose what we believe to be a novel hypothesis that a Bessel beam propagating through an optical system behaves identically to a paraxial ray under certain conditions. We then derive analytical formulas for the propagation of Bessel beams in Cartesian coordinates and the Huygens-Fresnel principle.
View Article and Find Full Text PDFPropensity Score Matching: should we use it in designing observational studies?
BMC Med Res Methodol
January 2025
Division of Public Health Sciences, Washington University in St Louis, 660 S. Euclid Ave, St Louis, MO, 63110, USA.
Background: Propensity Score Matching (PSM) stands as a widely embraced method in comparative effectiveness research. PSM crafts matched datasets, mimicking some attributes of randomized designs, from observational data. In a valid PSM design where all baseline confounders are measured and matched, the confounders would be balanced, allowing the treatment status to be considered as if it were randomly assigned.
View Article and Find Full Text PDFSoliton solutions of the (2 + 1)-dimensional Jaulent-Miodek evolution equation via effective analytical techniques.
Sci Rep
January 2025
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, 602105, India.
In this study, we investigate the [Formula: see text]-D Jaulent-Miodek (JM) equation, which is significant due to its energy-based Schrödinger potential and applications in fields such as optics, soliton theory, signal processing, geophysics, fluid dynamics, and plasma physics. Given its broad utility, a rigorous mathematical analysis of the JM equation is essential. The primary objective of this work is to derive exact soliton solutions using the Modified Sub-Equation (MSE) and Modified Auxiliary Equation (MAE) techniques.
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