Josephson Currents in Quantum Hall Devices

We consider a simple model for an SNS Josephson junction in which the "normal metal" is a section of a filling-factor $\nu=2$ integer quantum-Hall edge. We provide analytic expressions for the current/phase relations to all orders in the coupling between the superconductor and the quantum Hall edge modes, and for all temperatures. Our conclusions are consistent with the earlier perturbative study by Ma and Zyuzin [Europhysics Letters {\bf 21} 941-945 (1993)]: The Josephson current is independent of the distance between the superconducting leads, and the upper bound on the maximum Josephson current is inversely proportional to the perimeter of the Hall device.Comment: Revtex4. 22 pages 9 figures. Replaced version has minor typos fixed and one added referenc

Examining mean-field approximations and Bogoliubov-de Gennes (BdG) equations for topological quantum computing - some considerations on the conceptual basis of Majorana zero modes in p+ip superconductors

The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject

Estimation of swell height using spaceborne GNSS-R data from eight CYGNSS satellites

Global Navigation Satellite System (GNSS)-Reflectometry (GNSS-R) technology has opened a new window for ocean remote sensing because of its unique advantages, including short revisit period, low observation cost, and high spatial-temporal resolution. In this article, we investigated the potential of estimating swell height from delay-Doppler maps (DDMs) data generated by spaceborne GNSS-R. Three observables extracted from the DDM are introduced for swell height estimation, including delay-Doppler map average (DDMA), the leading edge slope (LES) of the integrated delay waveform (IDW), and trailing edge slope (TES) of the IDW. We propose one modeling scheme for each observable. To improve the swell height estimation performance of a single observable-based method, we present a data fusion approach based on particle swarm optimization (PSO). Furthermore, a simulated annealing aided PSO (SA-PSO) algorithm is proposed to handle the problem of local optimal solution for the PSO algorithm. Extensive testing has been performed and the results show that the swell height estimated by the proposed methods is highly consistent with reference data, i.e., the ERA5 swell height. The correlation coefficient (CC) is 0.86 and the root mean square error (RMSE) is 0.56 m. Particularly, the SA-PSO method achieved the best performance, with RMSE, CC, and mean absolute percentage error (MAPE) being 0.39 m, 0.92, and 18.98%, respectively. Compared with the DDMA, LES, TES, and PSO methods, the RMSE of the SA-PSO method is improved by 23.53%, 26.42%, 30.36%, and 7.14%, respectively.This work was supported in part by the National Natural Science Foundation of China under Grant 42174022, in part by the Future Scientists Program of China University of Mining and Technology under Grant 2020WLKXJ049, in part by the Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX20_2003, in part by the Programme of Introducing Talents of Discipline to Universities, Plan 111, Grant No. B20046, and in part by the China Scholarship Council (CSC) through a State Scholarship Fund (No. 202106420009).Peer ReviewedPostprint (published version

From Bench to Keyboard and Back Again: A Brief History of Lambda Phage Modeling

Cellular decision making is the process whereby cells choose one developmental pathway from multiple possible ones, either spontaneously or due to environmental stimuli. Examples in various cell types suggest an almost inexhaustible plethora of underlying molecular mechanisms. In general, cellular decisions rely on the gene regulatory network, which integrates external signals to drive cell fate choice. The search for general principles of such a process benefits from appropriate biological model systems that reveal how and why certain gene regulatory mechanisms drive specific cellular decisions according to ecological context and evolutionary outcomes. In this article, we review the historical and ongoing development of the phage lambda lysis–lysogeny decision as a model system to investigate all aspects of cellular decision making. The unique generality, simplicity, and richness of phage lambda decision making render it a constant source ofmathematical modeling–aided inspiration across all of biology. We discuss the origins and progress of quantitative phage lambda modeling from the 1950s until today, as well as its possible future directions. We provide examples of how modeling enabled methods and theory development, leading to new biological insights by revealing gaps in the theory and pinpointing areas requiring further experimental investigation. Overall, we highlight the utility of theoretical approaches both as predictive tools, to forecast the outcome of novel experiments, and as explanatory tools, to elucidate the natural processes underlying experimental data. </jats:p

2006: Can CGCMs simulate the Twentieth Century “warming hole” in the central United States

ABSTRACT The observed lack of twentieth-century warming in the central United States (CUS), denoted here as the &quot;warming hole,&quot; was examined in 55 simulations driven by external historical forcings and in 19 preindustrial control (unforced) simulations from 18 coupled general circulation models (CGCMs). Twentiethcentury CUS trends were positive for the great majority of simulations, but were negative, as observed, for seven simulations. Only a few simulations exhibited the observed rapid rate of warming (cooling) during 1901-40 (1940-79). Those models with multiple runs (identical forcing but different initial conditions) showed considerable intramodel variability with trends varying by up to 1.8°C century Ϫ1 , suggesting that internal dynamic variability played a major role at the regional scale. The wide range of trend outcomes, particularly for those models with multiple runs, and the small number of simulations similar to observations in both the forced and unforced experiments suggest that the warming hole is not a robust response of contemporary CGCMs to the estimated external forcings. A more likely explanation based on these models is that the observed warming hole involves external forcings combined with internal dynamic variability that is much larger than typically simulated. The observed CUS temperature variations are positively correlated with North Atlantic (NA) sea surface temperatures (SSTs), and both NA SSTs and CUS temperature are negatively correlated with central equatorial Pacific (CEP) SSTs. Most models simulate rather well the connection between CUS temperature and NA SSTs. However, the teleconnections between NA and CEP SSTS and between CEP SSTs and CUS temperature are poorly simulated and the models produce substantially less NA SST variability than observed, perhaps hampering their ability to reproduce the warming hole