There are several natural materials which have evolved functional gradients,ingeniously attaining maximal efficacy from limited components.Herein,we utilized the spatiotemporal distribution of initiator acetylacetone ...There are several natural materials which have evolved functional gradients,ingeniously attaining maximal efficacy from limited components.Herein,we utilized the spatiotemporal distribution of initiator acetylacetone to regulate the multienzyme polymerization and fabricate a chitosan-polymer hydrogel.The temporal priority order of acetylacetone was higher than phenolmodified chitosan by density functional theory calculation.The acetylacetone within the gelatin could gradually diffuse spatially into the chitosan hydrogel to fabricate the composite hydrogel with gradient network structure.The gradient hydrogel possessed a transferring topography from the two-dimensional pattern.A continuously decreased modulus along with acetylacetone diffusion was confirmed by atomic force microscope-based force mapping experiment.The water-retaining ability of various regions was confirmed by low-field nuclear magnetic resonance(NMR)and thermogravimetric analysis(TG)analysis,which led to the spontaneous actuation of gradient hydrogel with maximum 1821°/h curling speed and 227°curling angle.Consequently,the promising gradient hydrogels could be applied as intelligent actuators and flexible robots.展开更多
In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the co...In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the conditionp> max {1, 2N N+2 }is determined by the behaviour of u . Theorem implies that for solution in L N loc (Ω T ), the condition for the gradient of solution being H o¨ lder continuous needs only p>1 .展开更多
§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if...§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if展开更多
基金supported by the National Natural Science Foundation of China(51873156,51773155)the National Key Research and Development Program(2016YFA0100800)。
文摘There are several natural materials which have evolved functional gradients,ingeniously attaining maximal efficacy from limited components.Herein,we utilized the spatiotemporal distribution of initiator acetylacetone to regulate the multienzyme polymerization and fabricate a chitosan-polymer hydrogel.The temporal priority order of acetylacetone was higher than phenolmodified chitosan by density functional theory calculation.The acetylacetone within the gelatin could gradually diffuse spatially into the chitosan hydrogel to fabricate the composite hydrogel with gradient network structure.The gradient hydrogel possessed a transferring topography from the two-dimensional pattern.A continuously decreased modulus along with acetylacetone diffusion was confirmed by atomic force microscope-based force mapping experiment.The water-retaining ability of various regions was confirmed by low-field nuclear magnetic resonance(NMR)and thermogravimetric analysis(TG)analysis,which led to the spontaneous actuation of gradient hydrogel with maximum 1821°/h curling speed and 227°curling angle.Consequently,the promising gradient hydrogels could be applied as intelligent actuators and flexible robots.
文摘In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the conditionp> max {1, 2N N+2 }is determined by the behaviour of u . Theorem implies that for solution in L N loc (Ω T ), the condition for the gradient of solution being H o¨ lder continuous needs only p>1 .
文摘§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if