Results 1 to 10 of about 1,758 (174)
Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach [PDF]
Entropy, 2020 We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework.
Carlos Islas +2 more
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Computing Three-Dimensional Freeform Reflectors with a Scattering Surface [PDF]
EPJ Web of Conferences, 2023 We present a novel approach to computing reflectors with a scattering surface in illumination optics. A scattering model governed by a Fredholm integral equation is derived.
Kronberg Vì C.E. +3 more
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Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
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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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On some exact solutions of heavenly equations in four dimensions
AIP Advances, 2020 Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge–Ampère equations and of the second heavenly equation are found. Besides, non-invariance of the found classes of solutions of the
Ł. T. Stȩpień
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The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem [PDF]
Компьютерная оптика, 2018 We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge –
Nikolay Kazanskiy +3 more
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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations
Advanced Nonlinear Studies, 2020 In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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