Macroscopic energy diffusion for a chain of anharmonic oscillators

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space–time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and some upper and lower bounds.     

Ethylene/hindered phenol substituted norbornene copolymers: Synthesis and NMR structural determination

A new family of ethylene‐based copolymers with controlled amounts of a norbornene comonomer (N_ArOH) bearing a stabilizing antioxidant functionality (2,6‐di‐tert‐butyl phenol) was prepared. Due to unavoidable exo/endo equilibrium operative in N_ArOH comonomer, a complete and detailed NMR assignment of the structure of the prepared ethylene/N_ArOH copolymers was carried out for the determination of the exo/endo ratio inside the polymer. These novel functionalized comonomers can be considered suitable starting material for preparing ethylene‐based copolymers, with tunable comonomer content, as non‐releasing macromolecular antioxidant additives for specific application in safe food and/or drug packaging © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

SBV REGULARITY OF GENUINELY NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN ONE SPACE DIMENSION

The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a c...     

Capping [H<Subscript>8−n</Subscript>Ni<Subscript>42</Subscript>C<Subscript>8</Subscript>(CO)<Subscript>44</Subscript>]<Superscript>n−</Superscript> (n = 6, 7, 8) Octa-carbide Carbonyl Nanoclusters with [Ni(CO)] and [CuCl] Fragments

The reactions of [Ni₁₆(C₂)₂(CO)₂₃]^4? and [Ni₃₈C₆(CO)₄₂]^6? with CuCl afforded mixtures of the previously reported [HNi₄₂C₈(CO)₄₄(CuCl)]^7? bimetallic octa-carbide cluster and the new [HNi₄₃C₈(CO)₄₅]^7? and [HNi₄₄C₈(CO)₄₆]^7? homo-metallic octa-carbides. The three species have very similar properties resulting always in co-crystals such as [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·6.5MeCN (x = 0.14) (86% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 14%[HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?) and [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·5.5MeCN (x = 0.30) (70% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 30% [HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?). The new homo-metallic octa-carbides can be obtained free from the Ni–Cu octa-carbido cluster by reacting [Ni₁₀(C₂)(CO)₁₆]^2? in thf with a stoichiometric amount of CuCl, and crystals of [NMe₄]₆[H₂Ni_43+xC₈(CO)_45+x]·6MeCN (x = 0.72), which contain [H₂Ni₄₄C₈(CO)₄₆]^6? (72%) and [H₂Ni₄₃C₈(CO)₄₅]^6? (28%), have been obtained. Despite the different charges and compositions, these anions display almost identical structures, which are also closely related to those previously reported for the bimetallic Ni–Cd octa-carbido clusters [Ni_42+xC₈(CO)_44+x(CdCl)]^7? and [HNi_42+xC₈(CO)_44+x(CdBr)]^6?. Indeed, all these clusters are based on the same Ni₄₂C₈ cage decorated by miscellaneous [CdX]⁺ (X = Cl, Br), [CuCl] and [Ni(CO)] fragments.     

Coherent transfer by adiabatic passage in two-dimensional lattices

Coherent tunneling by adiabatic passage (CTAP) is a well-established technique for robust spatial transport of quantum particles in linear chains. Here we introduce two exactly-solvable models where the CTAP protocol can be extended to two-dimensional lattice geometries. Such bi-dimensional lattice models are synthesized from time-dependent second-quantization Hamiltonians, in which the bosonic field operators evolve adiabatically like in an ordinary three-level CTAP scheme thus ensuring adiabatic passage in Fock space.     

Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

Hydrophobic/hydrophilic P(VDF‐TrFE)/PHEA polymer blend membranes

Polymer blend membranes have been obtained consisting of a hydrophilic and a hydrophobic polymers distributed in co‐continuous phases. In order to obtain stable membranes in aqueous environments, the hydrophilic phase is formed by a poly(hydrohyethyl acrylate), PHEA, network while the hydrophobic phase is formed by poly(vinylidene fluoride‐co‐trifluoroethylene) P(VDF‐TrFE). To obtain the composites, in a first stage, P(VDF‐TrFE) is blended with poly(ethylene oxyde) (PEO), the latter used as sacrificial porogen. P(VDF‐TrFE)/PEO blend membranes were prepared by solvent casting at 70°C followed by cooling to room temperature. Then PEO is removed from the membrane by immersion in water obtaining a P(VDF‐TrFE) porous membrane. After removing of the PEO polymer, a P(VDF‐TrFE) membrane results in which pores are collapsed. Nevertheless the pores reopen when a mixture of hydroxethyl acrylate (HEA) monomer, ethyleneglycol dimethacrylate (as crosslinker) and ethanol (as diluent) is absorbed in the membrane and subsequent polymerization yields hybrid hydrophilic/hydrophobic membranes with controlled porosity. The membranes are thus suitable for lithium‐ion battery separator membranes and/or biostable supports for cell culture in biomedical applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 672–679