On multi-transitivity with respect to a vector

A topological dynamical system $(X,f)$ is said to be multi-transitive if for every $n\in\mathbb{N}$ the system $(X^{n}, f\times f^{2}\times \dotsb\times f^{n})$ is transitive. We introduce the concept of multi-transitivity with respect to a vector and show that multi-transitivity can be characterized by the hitting time sets of open sets, answering a question proposed by Kwietniak and Oprocha [On weak mixing, minimality and weak disjointness of all iterates, Erg. Th. Dynam. Syst., 32 (2012), 1661--1672]. We also show that multi-transitive systems are Li-Yorke chaotic.Comment: 11 page

Synthesis Of Thermo-Magneto-Responsive Poly(N-Isopropylacrylamide)-Based Composite Hydrogels For Adsorption-Desorption Of Chromium (Iii) Ions

Stimuli-responsive composite hydrogels have been in the vanguard of researches for their application in metal ion adsorption and its release via conformational change. The preparation of composite hydrogels with both thermo- and magneto-responsiveness requires careful layer-by-layer coatings of functional shells onto the core of iron oxide magnetic nanoparticles (MNPs). However, multiple stages of shell encapsulation of MNPs remains a major setback on the production of composite hydrogels with adequate colloidal stability and well-functioned dual-responsiveness. In this study, homo-polymeric poly(N-isopropylacrylamide)-encapsulated magnetite nanoparticles (PNIPAM-MNPs) cross-linked composite hydrogels were facilely synthesized via layer-by-layer coatings with and without employing silanization precursor, 3-(trimethoxysilyl)propyl methacrylate (MPS). It was found that PNIPAM could be gelated directly onto the silica-coated, poly(vinylpyrrolidone) (PVP) functionalized MNPs (silica-PVP-MNPs) via free radical polymerization without MPS to improve its colloidal stability and both thermo-magneto-responsive. Besides, co-polymeric poly(N-isopropylacrylamide-co-acrylic acid)-encapsulated MNPs ((PNIPAM-co-AA)-silica-PVP-MNPs) composite hydrogels were prepared for elucidating the difference in adsorption mechanisms between chelating groups of carboyxlates (-COO-) contained by AA moiety and amides (-CONH) of NIPAM moiety. In the temperature manipulated adsorption-desorption tests, desorption of Cr3+ gradually predominated as temperature increased from 298 K to 323 K for PNIPAMsilica-PVP-MNPs. Re-adsorption of Cr3+ by the composite hydrogel took place as being quenched to 298 K for lower initial Cr3+ concentration (20 – 80 mg L-1) which showed that desorption can be realised for surface adsorption. Before heating, the equilibrium adsorption data of Cr3+ fitted well into Flory-Huggins and Frumkin models, that elucidated the chelation of Cr3+ ions occurred via replacement of water molecules on the binding sites. Moreover, PNIPAM-silica-PVP-MNPs had higher maximum adsorption capacity, qm (434.78 mg g-1) compared to (PNIPAM-co-AA)-silica-PVP-MNPs (qm = 243.90 mg g-1) as extrapolated by Langmuir isotherm model in which the data of both composite hydrogels also showed good fit to the model. The adsorption kinetic analysis indicated that Cr3+ adsorption on PNIPAM-silica-PVP-MNPs was governed by intra-particle diffusion and reversible surface physisorption as its data followed pseudo-first, pseudo-second- and intra-particle diffusion models. On the other hand, surface chemisorption predominated over (PNIPAM-co-AA)-silica-PVP-MNPs as it followed only pseudo-second model

Edge states induce boundary temperature jump in molecular dynamics simulation of heat conduction

We point out that the origin of the commonly occurred boundary temperature jump in the application of No\'se-Hoover heat bath in molecular dynamics is related to the edge modes, which are exponentially localized at the edge of the system. If heat baths are applied to these edge regions, the injected thermal energy will be localized thus leading to a boundary temperature jump. The jump can be eliminated by shifting the location of heat baths away from edge regions. Following this suggestion, a very good temperature profile is obtained without increasing any simulation time, and the accuracy of thermal conductivity calculated can be largely improved.Comment: accepted by PRB, brief report, references added, typo correcte