An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic

A Novel Microspheres Composite Hydrogels Cross-linked by Methacrylated Gelatin Nanoparticles: Enhanced Mechanical Property and Biocompatibility

Content: Nowadays, protein-based nanoparticle as a biodegradable, biocompatible product attracts considerable interest for new uses in specialized technical areas. Gelatin is a denatured, biodegradable, and nonimmunogenic protein obtained by controlled hydrolysis of the triple-helix structure of collagen into single-strain molecules. As an amphiphilic biopolymer, gelatin can easily assemble into different kinds of aggregates under the defined pH and temperature and the resulting gelatin nanoparticles have been developed to be applied in the food industry and biomedical fields. Herein we report a novel macromolecular microsphere composites (MMC) hydrogels with the use of prepared methacrylated gelatin nanoparticles (MA-GNP) as the cross-linker. MA-GNP have the ability of chemical crosslinking by the polymerization of C=C bonds, such that the composite hydrogels can be formed by radical polymerization of acrylamide (AAm) on the surface of MA-GNP. The smooth spherical particles with an average size of ~100 nm have been synthesized through a modified two-step desolvation method as proved by atomic force microscopy (AFM). The results of nuclear magnetic resonance and dynamic light scattering further confirm the presence of reactive groups (C=C bonds) in the particles and its narrow sizes distribution. The resulting composite hydrogels (MA-GNP/PAAm) are porous materials with tunable pore sizes and exhibit enhanced compressive resistance and elasticity as well. Increasing appropriately the dosage of MA-GNP reduces the equilibrium swelling ratio and improves thermal stability of the gels. Moreover, all the hydrogels exhibit prolonged blood-clotting time, nonhemolytic nature and strong suitability for cell proliferation, indicating the improved antithrombogenicity and excellent cyto-compatibility. It suggests that the novel MA-GNP/PAAm hydrogels have potential application as tissue engineer scaffold materials, and the MA-GNP can be a promising macromolecular microsphere cross-linker for application in biomedical materials. The present work not only exploits new strategies to fabricate MMC hydrogels but also advance the potential application of biodegradable gelatin-based nanoparticles in biomedical fields. Take-Away: 1. A well-dispersed methacrylated gelatin nanoparticle (MA-GNP) with an average size of ~100 nm is presented by a modified two-step desolvation method. 2. MA-GNP is readily introduced into the polyacrylamide (PAAm) system as a cross-linker to prepare macromolecular microsphere composites (MMC) hydrogels via a free radical polymerization reaction. 3. MA-GNP is an effective cross-linker, improving both the compressive resistance and elasticity of MMC hydrogels as well as the biocompatibility

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer