Inverse problems related to electrical networks and the geometry of non-negative Grassmannians

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-09-19 DOI:10.1016/j.physd.2025.134948

A.A. Kazakov

引用次数: 0

Abstract

We provide a new solution to the classical black box problem (the discrete Calderón problem) in the theory of circular electrical networks. Our approach is based on the explicit embedding of electrical networks into non-negative Grassmannians and generalized chamber ansatz for it. Also, we reveal the relation of this problem with the combinatorial properties of spanning groves and the theory of totally non-negative matrices.

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与电网络相关的逆问题和非负格拉斯曼矩阵的几何

本文对圆形电网理论中的经典黑箱问题（离散Calderón问题）提出了一种新的解决方法。我们的方法是基于电网络的显式嵌入到非负的格拉斯曼和广义腔分析。同时，我们还揭示了该问题与生成树丛的组合性质和完全非负矩阵理论的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.