| 1. |
- Chen, Chuchu, et al.
(författare)
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Conservative methods for stochastic differential equations with a conserved quantity
- 2016
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Ingår i: International Journal of Numerical Analysis and Modeling. - Edmonton, Alberta, Canada. - 1923-2942. ; 13:3, s. 435-456
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Tidskriftsartikel (refereegranskat)abstract
- This paper proposes a novel conservative method for the numerical approximation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is 1 in the general case. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.
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| 3. |
- Yang, Xianpeng, et al.
(författare)
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Surface and Interface Engineering for Nanocellulosic Advanced Materials
- 2021
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Ingår i: Advanced Materials. - : Wiley. - 0935-9648 .- 1521-4095. ; 33:28
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Tidskriftsartikel (refereegranskat)abstract
- How do trees support their upright massive bodies? The support comes from the incredibly strong and stiff, and highly crystalline nanoscale fibrils of extended cellulose chains, called cellulose nanofibers. Cellulose nanofibers and their crystalline parts-cellulose nanocrystals, collectively nanocelluloses, are therefore the recent hot materials to incorporate in man-made sustainable, environmentally sound, and mechanically strong materials. Nanocelluloses are generally obtained through a top-down process, during or after which the original surface chemistry and interface interactions can be dramatically changed. Therefore, surface and interface engineering are extremely important when nanocellulosic materials with a bottom-up process are fabricated. Herein, the main focus is on promising chemical modification and nonmodification approaches, aiming to prospect this hot topic from novel aspects, including nanocellulose-, chemistry-, and process-oriented surface and interface engineering for advanced nanocellulosic materials. The reinforcement of nanocelluloses in some functional materials, such as structural materials, films, filaments, aerogels, and foams, is discussed, relating to tailored surface and/or interface engineering. Although some of the nanocellulosic products have already reached the industrial arena, it is hoped that more and more nanocellulose-based products will become available in everyday life in the next few years.
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