Strong,Thermally Superinsulating Biopolymer–Silica Aerogel Hybrids by Cogelation of Silicic Acid with Pectin

Silica aerogels are excellent thermal insulators, but their brittle nature has prevented widespread application. To overcome these mechanical limitations, silica–biopolymer hybrids are a promising alternative. A one‐pot process to monolithic, superinsulating pectin–silica hybrid aerogels is presented. Their structural and physical properties can be tuned by adjusting the gelation pH and pectin concentration. Hybrid aerogels made at pH 1.5 exhibit minimal dust release and vastly improved mechanical properties while remaining excellent thermal insulators. The change in the mechanical properties is directly linked to the observed “neck‐free” nanoscale network structure with thicker struts. Such a design is superior to “neck‐limited”, classical inorganic aerogels. This new class of materials opens up new perspectives for novel silica–biopolymer nanocomposite aerogels.     

Expanding discriminative dimensions for analysis and imaging

Eliminating the contribution of interfering compounds is a key step in chemical analysis. In complex media, one possible approach is to perform a preliminary separation. However purification is often demanding, long, and costly; it may also considerably alter the properties of interacting components of the mixture (e.g. in a living cell). Hence there is a strong interest for developing separation-free non-invasive analytical protocols. Using photoswitchable probes as labelling and titration contrast agents, we demonstrate that the association of a modulated monochromatic light excitation with a kinetic filtering of the overall observable is much more attractive than constant excitation to read-out the contribution from a target probe under adverse conditions. An extensive theoretical framework enabled us to optimize the out-of-phase concentration first-order response of a photoswitchable probe to modulated illumination by appropriately matching the average light intensity and the radial frequency of the light modulation to the probe dynamics. Thus, we can selectively and quantitatively extract from an overall signal the contribution from a target photoswitchable probe within a mixture of species, photoswitchable or not. This simple titration strategy is more specifically developed in the context of fluorescence imaging, which offers promising perspectives.     

Decimation of the Dyson–Ising ferromagnet

We study the decimation to a sublattice of half the sites of the one-dimensional Dyson–Ising ferromagnet with slowly decaying long-range pair potentials of the form $\frac{1}{{|i?j|}^{\alpha }}$, deep in the phase transition region ($1<\alpha \le 2$ and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ($\alpha >2$) and provides an example of a “standard” non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.     

Slipping zone location in squeeze flow

In squeeze flow rheometry, the main problem is the boundary condition between the squeezed material and the plates. Therefore, the crucial assumption is to know the location and the shape of the sample part where wall slip may or may not occur. This question is investigated from experimental results. For this, squeeze flow experiments are carried out to visualize the flow pattern at the walls. Influence of boundary conditions is particularly studied using different plate surface condition. As a result, with wall slipping conditions, we propose a flow modelling divided into two zones: a circular central zone of the sample sticks on the plates and, beyond that zone, the sample slips at the plates with friction.     

Optimal distribution of the internal null control for the one-dimensional heat equation

This paper addresses the problem of optimizing the distribution of the support of the internal null control of minimal L²-norm for the 1-D heat equation. A measure constraint is imposed on the support but no topological assumption such as the number of connected components. Therefore, the problem typically lacks of solution in the class of characteristic functions and needs of relaxation. We show that the relaxed formulation is obtained by replacing the set of characteristic functions by its convex envelope. The proof requires that the observability constant related to the control problem be uniform with respect to the support, property which is obtained by the control transmutation method. The optimality conditions of the relaxed problem as well as the case where the number of connected components is fixed a priori are also discussed. Several numerical experiments complete the study and suggest the ill-posedness of the problem in contrast to the wave situation.     

Complexity issues for the sandwich homogeneous set problem

Graph sandwich problems were introduced by Golumbic et al. (1994) in [12] for DNA physical mapping problems and can be described as follows. Given a property Π of graphs and two disjoint sets of edges E₁, E₂ with E₁⊆E₂ on a vertex set V, the problem is to find a graph G on V with edge set E_s having property Π and such that E₁⊆E_s⊆E₂.In this paper, we exhibit a quasi-linear reduction between the problem of finding an independent set of size k≥2 in a graph and the problem of finding a sandwich homogeneous set of the same size k. Using this reduction, we prove that a number of natural (decision and counting) problems related to sandwich homogeneous sets are hard in general. We then exploit a little further the reduction and show that finding efficient algorithms to compute small sandwich homogeneous sets would imply substantial improvement for computing triangles in graphs.     

Ergodic BSDEs under weak dissipative assumptions

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate.We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of “Markovian” solutions by exploiting the recurrence of the same class of forward equations.Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.     

60]Fullerene-based monolayers as neuroprotective biocompatible hybrid materials

Here we report on the surface immobilization of redox-active [60]fullerene derivatives and the consequent neuroprotective effects toward l-glutamate induced excitotoxicity in human derived undifferentiated neuroblastoma cells.