We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to O(N ) per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

Off-site construction has been increasingly employed due to its advantages, for instance, improved quality control, reduced skills labour, faster construction time, decreased material wastage and safe working environment. As the most cutting-edge off-site construction, modular buildings have been utilised for residential building, student accommodation, and hotel projects. However, because of existing and underlying constraints, the adoption of modular buildings is still relatively low. To reveal factors hindering the development of high-rise modular buildings, a comprehensive literature review, coupled with a focus group study, were conducted. A questionnaire survey inquiring about all stakeholders was implemented to quantify constraints. The results were further examined according to a real-life case study. This paper manifested that “Lack of coordination and communication among stakeholders”, “Higher cost”, “Lack of government support”, “Lack of experience and expertise”, “Lack of building codes and standards”, “Poor supply chain integration”, and “Complexity of connection” are the top barriers curbing the uptake of modular buildings. The findings should provide a valuable reference for stakeholders adopting modular buildings, whilst mitigating risks amid modular construction. Future research is expected to exploit building information modelling and design for manufacture and assembly to alleviate these existing constraints and promote the performance of modular construction as well.

We seek to establish qualitative convergence results to a general class of evolution PDEs described by gradient flows in optimal transportation distances. These qualitative convergence results come from dynamical systems under the general name of LaSalle Invariance Principle. By combining some of the basic notions of gradient flow theory and dynamical systems, we are able to reproduce this invariance principle in the setting of evolution PDEs under general assumptions. We apply this abstract theory to a non-exhaustive list of examples that recover, simplify, and even extend the results in their respective literatures.

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Information exchange between building information modelling (BIM) and geographic information system (GIS) is problematic, especially in terms of semantic information. Graph-based technologies, such as the resource description framework (RDF) and the labelled property graph (LPG), are promising in solving this problem. These two technologies are different but have not been systematically investigated in the context of BIM/GIS integration. This paper presents our systematic investigation into these two technologies, trying to propose the proper one for BIM/GIS data integration. The main findings are as follows. (1) Both LPG-based databases and RDF-based databases can be generally considered graph databases, but an LPG-based database is considered a native graph database, while an RDF-based database is not. (2) RDF suits applications focusing more on linking data and sharing data, and (3) LPG-based graph database suits applications focusing more on data query and analysis. An LPG-based graph database is thus proposed for BIM/GIS data integration. This review can facilitate the use of graph technology in BIM/GIS integration.

We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker-Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the Γ-convergence of gradient flows technique introduced by Sandier and Serfaty [37,39]. In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation.

We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to make sense of the particle solutions. These particle solutions solve a large coupled ODE system that retains all the important properties of the Landau operator, namely the conservation of mass, momentum and energy, and the decay of entropy. We illustrate our new method by showing its performance in several test cases including the physically relevant case of the Coulomb interaction. The comparison to the exact solution and the spectral method is strikingly good maintaining 2nd order accuracy. Moreover, an efficient implementation of the method via the treecode is explored. This gives a proof of concept for the practical use of our method when coupled with the classical PIC method for the Vlasov equation.