Characterizing bearing equivalence in directed graphs

In this paper, we study bearing equivalence in directed graphs. We first give a strengthened definition of bearing equivalence based on the \textit{kernel equivalence} relationship between bearing rigidity matrix and bearing Laplacian matrix. We then present several conditions to characterize bearing equivalence for both directed acyclic and cyclic graphs. These conditions involve the spectrum and null space of the associated bearing Laplacian matrix for a directed bearing formation. For directed acyclic graphs, all eigenvalues of the associated bearing Laplacian are real and nonnegative, while for directed graphs containing cycles, the bearing Laplacian can have eigenvalues with negative real parts. Several examples of bearing equivalent and bearing non-equivalent formations are given to illustrate these conditions.Comment: Accepted by the 22nd World Congress of the International Federation of Automatic Contro

Probe nuclear structure using the anisotropic flow at the Large Hadron Collider

Recent studies have shown that the shape and radial profile of the colliding nuclei have strong influences on the initial condition of the heavy ion collisions and the subsequent development of the anisotropic flow. Using A Multi-Phase Transport model (AMPT) model, we investigated the impact of nuclear quadrupole deformation $\beta_2$ and nuclear diffuseness $a_0$ of $^{129}$Xe on various of flow observables in Xe--Xe collisions at \sqrtnn = 5.44 TeV. We found that $\beta_2$ has a strong influence on central collisions while $a_0$ mostly influences the mid-central collisions. The relative change of flow observables induced by a change in $\beta_2$ and $a_0$ are also found to be insensitive to the values of parameters controlling the strength of the interaction among final state particles. Our study demonstrates the potential for constraining the initial condition of heavy ion collisions using future system scans at the LHC.Comment: 25 pages, for the EPJA Topical Issue

Responsive Emulsions for Sequential Multienzyme Cascades

Multienzyme cascade biocatalysis is an efficient synthetic process, avoiding the isolation/purification of intermediates and shifting the reaction equilibrium to the product side. However, multienzyme systems are often limited by their incompatibility and cross‐reactivity. Herein, we report a multi‐responsive emulsion to proceed multienzyme reactions sequentially for high reactivity. The emulsion is achieved using a CO2, pH, and thermo‐responsive block copolymer as a stabilizer, allowing the on‐demand control of emulsion morphology and phase composition. Applying this system to a three‐step cascade reaction enables the individual optimal condition for each enzyme, and a high overall conversion (ca. 97 % of the calculated limit) is thereby obtained. Moreover, the multi‐responsiveness of the emulsion allows the facile and separate yielding/recycling of products, polymers and active enzymes. Besides, the system could be scaled up with a good yield