Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers and frequency combs. However, due to the local nature of nonlinearities, previous attempts to classify the topology of nonlinear systems have required significant approximations that must be tailored to individual systems. Here, we develop a general framework for classifying the topology of nonlinear materials in any discrete symmetry class and any physical dimension. Our approach is rooted in a numerical K-theoretic method called the spectral localizer, which leverages a real-space perspective of a system to define local topological markers and a local measure of topological protection. Our nonlinear spectral localizer framework yields a quantitative definition of topologically non-trivial nonlinear modes that are distinguished by the appearance of a topological interface surrounding the mode. Moreover, we show how the nonlinear spectral localizer can be used to understand a system's topological dynamics, i.e., the time-evolution of nonlinearly induced topological domains within a system. We anticipate that this framework will enable the discovery and development of novel topological systems across a broad range of nonlinear materials
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FlashRoute: Efficient Traceroute on a Massive Scale
We propose a new traceroute tool, FlashRoute for efficient large-scale topology discovery. FlashRoute reduces the time required for tracerouting the entire /24 IPv4 address space by a factor of three and half compared to previous state of the art. Additionally, we present a new technique to measure hop-distance to a destination using a single probe and uncover a bias of the influential ISI Census hitlist [18] in topology discovery.
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- Award ID(s):
- 1647145
- NSF-PAR ID:
- 10227490
- Date Published:
- Journal Name:
- Proceedings of the ACM Internet Measurement Conference
- Page Range / eLocation ID:
- 443 to 455
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3419394.3423619
