A Schauder estimate for stochastic PDEs

Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate. As an application, the existence and uniqueness of solution to the Cauchy problem is also proved.Comment: This is an abridged version. A full version is submitted separatel

Application of CFD, Taguchi Method, and ANOVA Technique to Optimize Combustion and Emissions in a Light Duty Diesel Engine

Some previous research results have shown that EGR (exhaust gas recirculation) rate, pilot fuel quantity, and main injection timing closely associated with engine emissions and fuel consumption. In order to understand the combined effect of EGR rate, pilot fuel quantity, and main injection timing on the NOx (oxides of nitrogen), soot, and ISFC (indicated specific fuel consumption), in this study, CFD (computational fluid dynamics) simulation together with the Taguchi method and the ANOVA (analysis of variance) technique was applied as an effective research tool. At first, simulation model on combustion and emissions of a light duty diesel engine at original baseline condition was developed and the model was validated by test. At last, a confirmation experiment with the best combination of factors and levels was implemented. The study results indicated that EGR is the most influencing factor on NOx. In case of soot emission and ISFC, the greatest influence parameter is main injection timing. For all objectives, pilot fuel quantity is an insignificant factor. Furthermore, the engine with optimized combination reduces by at least 70% for NOx, 20% in soot formation, and 1% for ISFC, in contrast to original baseline engine

On The Cauchy Problem For Stochastic Parabolic Equations In Holder Spaces

In this paper, we establish a sharp $C^{2+\alpha }$-theory for stochastic partial differential equations of parabolic type in the whole space

Stochastic hölder continuity of random fields governed by a system of stochastic PDEs

Association des Publications de l\u27Institut Henri Poincaré, 2020. This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain Hölder-type classes in which a random field is treated as a space-time function taking values in Lp-space of random variables. A modified stochastic parabolicity condition involving p is proposed to ensure the finiteness of the associated norm of the solution, which is showed to be sharp by examples. The Schauder-type estimates and the solvability theorem are proved

Magnetic and superconducting properties of spin-fluctuation-limited superconducting nanoscale VNx

VN x nanoparticles and nanowires have been prepared by nitrifying V 2O 5 nanoparticles (NP) and nanowires (NW). The V 2O 5 NP and NW were synthesized by a facile hydrothermal method. Magnetic susceptibility (X) and magnetization measurements showed long range superconducting ordering (LRSO) at the temperature of 5.8 K for NW, but there was no observation of LRSO (at least down to 2 K) for the NP sample, which is a much lower temperature than for the corresponding bulk, while both NP and NW showed the absence of long range magnetic ordering, at least down to 2 K. However, X the data showed that both samples possess a high Pauli-like component, X 0, in their susceptibility (X 0 ≈ 2.22 × 10 -4emu/mol for NP and 5 × 10 -4emu/mol for NW). Moreover, for the NW samples, X has a strong magnetic field dependence and presents a non-linear field-polarization feature, suggesting strong spin-orbit coupling

Influence of root distribution on preferential flow in deciduous and coniferous forest soils

Root-induced channels are the primary controlling factors for rapid movement of water and solute in forest soils. To explore the effects of root distribution on preferential flow during rainfall events, deciduous (Quercus variabilis BI.) and coniferous forest (Platycladus orientalis (L.) Franco) sites were selected to conduct dual-tracer experiments (Brilliant Blue FCF and Bromide [Br-]). Each plot (1.30 × 1.30 m) was divided into two subplots (0.65 × 1.30 m), and two rainfall simulations (40 mm, large rainfall and 70 mm, extreme rainfall) were conducted in these. Vertical soil profiles (1.00 m × 0.40 m) were excavated, and preferential flow path features were quantified based on digital image analysis. Root (fine and coarse) abundance and Br- concentration were investigated for each soil profile. In deciduous forest, accumulated roots in the upper soil layer induce larger lateral preferential flow as compared to the coniferous forest soil during large rainfall events. Compared with deciduous forest, coniferous forest soil, with higher (horizontal and vertical) spatial variability of preferential flow paths, promotes higher percolation and solute leaching to deeper soil layers during extreme rainfall events. Fine roots, accounting for a larger proportion of total roots (compared to coarse roots), facilitate preferential flow in the 0-40 cm forest soil layer. Overall, our results indicate that the root distribution pattern of different tree species can exert diverse effects on preferential flow in forest soils