Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations

This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook) schemes in the framework of finite volume method for the ultra-relativistic flows. Different from the existing kinetic flux-vector splitting (KFVS) or BGK-type schemes for the ultra-relativistic Euler equations, the present genuine BGK schemes are derived from the analytical solution of the Anderson-Witting model, which is given for the first time and includes the "genuine" particle collisions in the gas transport process. The BGK schemes for the ultra-relativistic viscous flows are also developed and two examples of ultra-relativistic viscous flow are designed. Several 1D and 2D numerical experiments are conducted to demonstrate that the proposed BGK schemes not only are accurate and stable in simulating ultra-relativistic inviscid and viscous flows, but also have higher resolution at the contact discontinuity than the KFVS or BGK-type schemes.Comment: 41 pages, 13 figure

Design of two-dimensional material-based electrocatalysts via hetero-interface engineering

With ever-increasing concern about energy crisis, environmental pollution, and climate change, seeking for clean and renewable energy sources has become one of the biggest challenges for the sustainable development of society. The key to address this concern is the development of advanced energy conversion technologies, such as water electrolysis for hydrogen generation, fuel cells, and metal-air batteries. Developing high-efficient electrocatalysts for the next-generation energy conversion devices has become a primary focus of research. Since two-dimensional (2D) graphene was discovered, numerous 2D nanomaterials have aroused more research interest in the fields of energy conversion and storage. In particular, the novel 2D nanomaterials have become one of the most promising components for design and development of heterogenous electrocatalysts because of their unique physicochemical properties and adjustable electronic structure. However, some 2D nanomaterials are not active enough because of the large reaction free energy, low amount of active sites or poor conductivity. Some 2D materials are inert for electrocatalysis reactions, but are able to work as the functional substrates for the development of hybrid electrocatalysts. Thus, specific strategies are urgently desired to modulate the physicochemical and surface/interface properties of 2D material-based electrocatalysts, and to make full use of the functionalities of functional 2D material substrates to achieve fast catalytic reaction kinetics. In this regard, hetero-interface engineering strategy has been deployed into designing and preparing three different 2D material-based elctrocatalysts with well-defined interfaces for the enhanced oxygen evolution reaction (OER), hydrogen evolution reaction (HER), and oxygen reduction reaction (ORR). For the first work, the superhydrophilic GCN/Ni(OH)2 (GCNN) heterostructures with monodispersed Ni(OH)2 nanoplates strongly anchored on GCN were synthesized for enhanced water oxidation catalysis. Owing to the superhydrophilicity of functionalized GCN, the surface wettability of GCNN (contact angle 0°) was substantially improved as compared with bare Ni(OH)2 (contact angle 21°). Besides, GCN nanosheets can effectively suppress Ni(OH)2 aggregation to help expose more active sites. Benefiting from the well-defined catalyst surface, the optimal GCNN hybrid showed a significantly enhanced electrochemical performance over bare Ni(OH)2 nanosheets, although GCN is electrochemically inert. In addition, similar performance promotion resulting from wettability improvement induced by the incorporation of hydrophilic functionalized GCN was also successfully demonstrated on Co(OH)2..

Enabling Multi-level Trust in Privacy Preserving Data Mining

Privacy Preserving Data Mining (PPDM) addresses the problem of developing accurate models about aggregated data without access to precise information in individual data record. A widely studied \emph{perturbation-based PPDM} approach introduces random perturbation to individual values to preserve privacy before data is published. Previous solutions of this approach are limited in their tacit assumption of single-level trust on data miners. In this work, we relax this assumption and expand the scope of perturbation-based PPDM to Multi-Level Trust (MLT-PPDM). In our setting, the more trusted a data miner is, the less perturbed copy of the data it can access. Under this setting, a malicious data miner may have access to differently perturbed copies of the same data through various means, and may combine these diverse copies to jointly infer additional information about the original data that the data owner does not intend to release. Preventing such \emph{diversity attacks} is the key challenge of providing MLT-PPDM services. We address this challenge by properly correlating perturbation across copies at different trust levels. We prove that our solution is robust against diversity attacks with respect to our privacy goal. That is, for data miners who have access to an arbitrary collection of the perturbed copies, our solution prevent them from jointly reconstructing the original data more accurately than the best effort using any individual copy in the collection. Our solution allows a data owner to generate perturbed copies of its data for arbitrary trust levels on-demand. This feature offers data owners maximum flexibility.Comment: 20 pages, 5 figures. Accepted for publication in IEEE Transactions on Knowledge and Data Engineerin

A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraint-preserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten--Lax--van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method.Comment: 56 pages, 18 figure