We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger-Kantorovich problem (), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton-Jacobi equation arising in the dual dynamic formulation of , which are sufficiently strong to construct a characteristic transport-growth flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow. Finally, exact conditions for functionals defined on the space of measures are derived that guarantee the geodesic -convexity with respect to the Hellinger-Kantorovich distance. Examples of geodesically convex functionals are provided.
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http://dx.doi.org/10.1007/s00205-023-01941-1 | DOI Listing |
Sci Rep
January 2025
National Institutes for Quantum Science and Technology, Kamikita, 039-3212, Japan.
The Alfvén instability nonlinearly excited the energetic-particle-driven geodesic acoustic mode on the ASDEX-Upgrade tokamak, as demonstrated experimentally. The mechanism of the energetic-particle-driven geodesic acoustic mode excitation and the mode nonlinear evolution is not yet fully understood. In the present work, a first-principles simulation using the MEGA code investigated the mode properties in both the linear growth and nonlinear saturated phases.
View Article and Find Full Text PDFJ Acoust Soc Am
December 2024
Key Laboratory for Polar Acoustics and Application of Ministry of Education (Harbin Engineering University), Ministry of Education, Harbin, 150001, China.
Matched-field processing (MFP) achieves underwater source localization by measuring the correlation between the array and replica signals, with traditional MFP being equivalent to estimating the Euclidean distance between the data cross-spectral density matrix (CSDM) and replica matrices. However, in practical applications, random inhomogeneities in the marine environment and inaccurate estimation of CSDM reduce MFP performance. The traditional minimum variance matched-field processor with environmental perturbation constraints perturbs a priori environment parameters to obtain linear constraints and yields the optimal weight vectors as the replica vectors.
View Article and Find Full Text PDFHeliyon
October 2024
Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa.
This study investigates the Lie symmetry properties of matter variables, spacetime dimension, and kinematic quantities in spherically symmetric radiating stars undergoing gravitational collapse in higher dimensional spacetimes. Our analysis explores how variations in functions and dependent variables influence the Lie algebra dimensionality and Lie symmetries of the boundary condition. Our study reveals the explicit dependence of charge and spacetime dimension in the Lie symmetry generators for the first time.
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December 2024
Yale Institute for Network Science, Yale University, New Haven, CT, USA.
Consensus formation is a complex process, particularly in networked groups. When individuals are incentivized to dig in and refuse to compromise, leaders may be essential to guiding the group to consensus. Specifically, the relative geodesic position of leaders could be important for reaching consensus.
View Article and Find Full Text PDFGeom Dedic
September 2024
Department of Mathematics, KU Leuven, Celestijnenlaan 200B - box 2400, 3001 Leuven, Belgium.
Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse entropy and that this value is a coarse invariant.
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