arXiv subjects

Zhiwei Yan

Publications and source records attributed to Zhiwei Yan.

3 recordsLinked to original sources

arXiv2025

The space of unital algebra homomorphisms $C^\infty(S)\to\Lambda_2$: a singular determinantal model

Let $\Lambda_2$ be the real Grassmann algebra on two odd generators. Define $\mathcal{J}(S)$ as the set of unital algebra homomorphisms $C^\infty(S)\to \Lambda_2$ that are not required to preserve parity. This space is motivated by replacing the commutative local test algebra appearing in Weil's near-point construction with $\Lambda_2$. Each homomorphism expands to give a base point and three tangent vectors. The homomorphism condition, together with the noncommutativity of $\Lambda_2$, forces two of these tangent vectors to be linearly dependent. The resulting parameter space is $\mathcal{C}(TS) \times_S TS$, where $\mathcal{C}(TS)$ is the fibrewise determinantal cone of pairs of linearly dependent tangent vectors. When $\dim S \ge 2$, $\mathcal{J}(S)$ carries fibrewise conical singularities along its zero section; when $\dim S = 1$, $\mathcal{J}(S)$ is a smooth manifold.

math.DG↗

arXiv2024

A conformal mapping approach to broadband nonlinear optics on chip

Integrated nonlinear optical devices play an important role in modern optical communications. However, conventional on-chip optical devices with homogeneous or periodic translation dimensions generally have limited bandwidth when applied to nonlinear optical applications. Up today, there lacks a general method to design compact nonlinear optical devices over a broadband continuous frequency range. In this work, we propose a general strategy based on transformation optics (TO) to design curved accelerating waveguides (CAWs) with spatially gradient curvatures able to achieve broadband nonlinear frequency conversion on chip. Through rigorous analytical calculation, we show that increasing the acceleration (i.e. gradient in the waveguide curvature) broadens the output signal spectrum in the nonlinear process. In the experiment, we take the sum-frequency generation for infrared signal upconversion (SFG-ISU) as the example and fabricated a variety of CAWs using thin-film lithium niobate on insulator (LNOI). Efficient SFG is observed over a broadband continuous spectrum. Our conformal mapping approach offers a platform for various nonlinear optical processes and works in any frequency range, including visible, infrared and terahertz bands. Apart from LNOI, our approach is also compatible with other nonlinear materials, such as silicon, silicon nitride and chalcogenide glasses etc.

physics.optics↗

arXiv2018

An experiment in distributed Internet address management using blockchains

The current system to manage the global pool of IP addresses is centralized in five transnational organizations, the Regional Internet Registries (RIRs). Each of these RIRs manage the address pool for a large number of countries. Because the RIRs are private organizations, they are subject to the legal framework of the country where they are based. This configuration results in a jurisdictional overflow from the legal framework of the countries where the RIR is based to all the countries that the RIRs are serving (the countries served by the RIRs de facto become subjects of the legal system of the country where the RIR is hosted). The situation is aggravated by the deployment of new security techniques such as the RPKI and BGPsec, that enable enforcement of allocations by the RIRs. In this paper we present InBlock, a blockchain-based distributed governance body aimed to provide de-centralized management of IP addresses. InBlock also aims to fulfil the same objectives as the current IP address allocation system, namely, uniqueness, fairness, conservation, aggregation, registration and minimized overhead. InBlock is implemented as a Decentralized Autonomous Organization, i.e., as a set of blockchain's smart contracts in Ethereum. Any entity may request an allocation of addresses to the InBlock registry by solely performing a (crypto)currency transfer to the InBlock. The fee required, along with the annual renewal fee, serves as a mechanism to deter stockpiling and other wasteful practices. As with any novel technology, there are many open questions about the usage of blockchains to build an IP address registry. For this reason, we believe that practical experimentation is required in order to have hands-on experiences about such a system. We propose to conduct an experiment on distributed address management using InBlock as a starting point to inform future directions in this area.

cs.NI↗