Results 11 to 20 of about 8,395 (199)
IET Microwaves, Antennas & Propagation, 2023 This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non ...
Aline Rocha deAssis +2 more
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CAAI Transactions on Intelligence TechnologyMonge–Ampère equations (MAEs) are fully nonlinear second‐order partial differential equations (PDEs), which are closely related to various fields including optimal transport (OT) theory, geometrical optics and affine geometry. Despite their significance,
Xinghua Pan, Zexin Feng, Kang Yang
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]
Quant BiolAbstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
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Monotone discretization of the Monge-Ampère equation of optimal transport
ESAIM: Mathematical Modelling and Numerical Analysis, 2022 We design a monotone finite difference discretization of the second boundary value problem for the Monge-Ampère equation, whose main application is optimal transport.
G. Bonnet, J. Mirebeau
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The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary [PDF]
Calculus of Variations and Partial Differential Equations, 2021 We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge–Ampère equation on a general Hermitian manifold with non-empty boundary.
S. Kołodziej, N. Nguyen
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Design of optical surfaces conform the hyperbolic Monge-Ampère equation [PDF]
EPJ Web of Conferences, 2022 We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface.
Bertens M.W.M.C. +3 more
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Freeform design of a two-reflector system to collimate and shape a point source distribution [PDF]
EPJ Web of Conferences, 2021 We present a method to design a freeform two-reflector system to collimate and shape a beam from a point source. An important generalization compared to previous research is that the output beam can be in an arbitrary direction.
van Roosmalen A.H. +3 more
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Advances in Nonlinear Analysis, 2021 In this paper, we establish the second boundary behavior of the unique strictly convex solution to a singular Dirichlet problem for the Monge-Ampère ...
Wan Haitao, Shi Yongxiu, Liu Wei
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An adaptive least-squares algorithm for the elliptic Monge–Ampère equation
Comptes Rendus. Mécanique, 2023 We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach.
Caboussat, Alexandre +2 more
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A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation
Mathematics in Engineering, 2022 We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.
Yu Yuan
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