Synthesis of models of metabolites: Oxidation of variously substituted chromenes including acronycine,by a porphyrin catalytic system

The influence of chemical neighbouring on oxidation of substituted 2,2‐dimethylchromenes derivatives 5‐8 by a biomimetic catalytic system was first studied. It was then applied to acronycine an anti‐cancer drug in order to obtain in one single step oxidized products resulting from the reactivity of the 1,2‐double bond in the pyranic D‐ring. These 2,2‐dimethylchromenes constitute the structural moiety responsible for the activity of acronycine. This oxidation showed the sensitivity of the ethylenic bond, leading to the formation of the corresponding epoxides, diols and/or ketoalcohol. In the case of 5‐dimethylamino‐2,2‐dimethylchromene 8 , the double bond was not sensitive to oxidation, but the N‐methyl groups reacted to lead to the formamide derivative 16 and an imino‐alcohol 17 . This methodology applied to acronycine molecule 1 , allowed to obtain in one step, two oxidized compounds, a trans‐diol 3 and a ketoalcohol 4 under preparative conditions.     

A posteriori error estimation for the Stokes–Darcy coupled problem on anisotropic discretization

This paper presents an a posteriori error analysis for the stationary Stokes–Darcy coupled problem approximated by finite element methods on anisotropic meshes in or 3. Korn's inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to non‐conforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for non‐conforming case. With the obtained finite element solutions, the error estimators are constructed and based on the residual of model equations plus the stabilization terms. The lower error bound is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so‐called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media. Copyright © 2016 John Wiley & Sons, Ltd.     

Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential

We study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter $\lambda \rightarrow 0$ , and the anharmonicity by a parameter $\lambda ^{\prime } \le \lambda $ . Let $\kappa $ be the conductivity of the chain, defined through the Green–Kubo formula. Under suitable hypotheses, we show that $\kappa = \mathcal O (\lambda )$ and, in the absence of anharmonic potential, that $\kappa \sim \lambda $ . This is in sharp contrast with the ordered chain for which $\kappa \sim 1/\lambda $ , and so shows the persistence of localization effects for a non-integrable dynamics.     

Thermal Conductivity for a Momentum Conservative Model

We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like t ^−d/2 in the unpinned case and like t ^−d/2–1 if an on-site harmonic potential is present. This implies a finite conductivity in d ≥ 3 or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.     

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.     

Global invariants and equilibrium states in lattice gases

It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forL ^k. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofL ^k which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure.     

Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities

We consider the stationary states of a chain of n anharmonic coupled oscillators, whose deterministic Hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature T _ℓ and T _r and subject to constant forces τ _ℓ and τ _r . If the forces differ τ _ℓ ≠τ _r the center of mass of the system will move of a speed V _s inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-Kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.