Two-dimensional LWR model for lane-free traffic

While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and no lane discipline. We propose a first-order two-dimensional Lighthill-Whitham-Richards (LWR) model for the continuous macroscopic longitudinal and lateral dynamics of this type of traffic flow. The continuity equation is extended into two dimensions and the equation is closed by assuming a longitudinal flow-density relationship as in traditional one-dimensional models while the lateral dynamics is based on boundary repulsion and a desire of a majority of the drivers to go to less dense regions. This is equivalent to Fick's law giving rise to a lateral diffusion term. Using the proposed model, several numerical tests were conducted under different traffic scenarios representing a wide range of traffic conditions. Even for extreme initial conditions, the model's outcome turned out to be plausible and consistent with observed traffic flow dynamics. Moreover, the numerical convergence test is performed using an analytical solution for lateral steady-state conditions. The model was applied for bicycle simulation and reproduced the evolution of lateral density profile with asymmetric behavior

Structural determination of Enzyme-Graphene Nanocomposite Sensor Material

State-of-the-art ultra-sensitive blood glucose-monitoring biosensors, based on glucose oxidase (GOx) covalently linked to a single layer graphene (SLG), will be a valuable next generation diagnostic tool for personal glycemic level management. We report here our observations of sensor matrix structure obtained using a multi-physics approach towards analysis of small-angle neutron scattering (SANS) on graphene- based biosensor functionalized with GOx under different pH conditions for various hierarchical GOx assemblies within SLG. We developed a methodology to separately extract the average shape of GOx molecules within the hierarchical assemblies. The modeling is able to resolve differences in the average GOx dimer structure and shows that treatment under different pH conditions lead to differences within the GOx at the dimer contact region with SLG. The coupling of different analysis methods and modeling approaches we developed in this study provides a universal approach to obtain detailed structural quantifications, for establishing robust structure-property relationships. This is an essential step to obtain an insight into the structure and function of the GOx-SLG interface for optimizing sensor performance