A Novel Accurate Method forMulti-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains

Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity.For(1+1)-dimensional problems,analytical solutions that satisfy the boundary requirements are derived.Such solutions are numerically calculated using the trigonometric basis approximation for(2+1)-dimensional problems.With the aid of these analytical or numerical approximations,the original problems can be converted into the fractional ordinary differential equations,and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients.An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems.The straightforward quasilinearization technique is applied to handle nonlinear issues.Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.

The Curing for Modified Vinyl Ester Resin by Hexamethylene Diisocyanate and Its Influence on Performances

The commercial vinyl ester resins(VER)was modified by diphenylmethane diisocyanate(MDI)to enhance its toughness,which is called MVER.Hexamethylene diisocyanate(HDI),a common curing agent for polyurethane(PU),was found to be a reactive agent for MVER and can contribute to the toughness of MVER.Based on present experiment results,the crosslinking mechanism of MVER and HDI system is very similar to that of PU.The FTIR result shows the-NCO of HDI can react with the-OH of MVER.The microstructure of material prepared by MVER and HDI was characterized by NMR,and it was revealed that the unique microstructure leads to the good performances.The different content of HDI has an influence on the microstructure,and the microstructure gradually reduces the toughness and mechanical performances of the MVER cured with increasing concentration of reactive curing agent(HDI).This feature is consistent with a maximum in toughness as a function of the additive(HDI)content,followed by a rapid deterioration in toughness at higher concentrations.The toughness exhibits the maximum at such an HDI concentration(20wt%).Therefore,the special curing agent(HDI)and reactive mode is very important to the microstructure and mechanical properties of material.Furthermore,there should be other reactions which contribute to the curing and microstructure of the material,which needs the further research.