Sub-radiation versus super-radiation from a system of a spatially distributed two-level atoms

We study exactly solvable Dicke-like model describing a system of spatially distributed two-level atoms coupled to a single mode cavity field. We study the model in one excitation sub-space, when the field is supposed to be initially in the vacuum state and just one atom of the atomic sample is excited. We show that depending on the particular spatial distribution of atoms the system under consideration can exhibit super-radiation or subradiation. Moreover, we investigate the dynamics of the two-atom system interacting with the cavity field initially prepared in an arbitrary state. Co-operative effects are discussed in this case.     

Epoxidation of cyclohexene on modified Ti-containing mesoporous MCM-41

Ti-MCM-41, B-Ti-MCM-41 and Ti-grafted MCM-41 were synthesized, characterized and studied in the epoxidation of cyclohexene. The synthetic methods and the effect of water in the oxidant are discussed.     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Cooperative Crystallization of Heterometallic Indium–Chromium Metal–Organic Polyhedra and Their Fast Proton Conductivity

Metal–organic polyhedra (MOPs) or frameworks (MOFs) based on Cr³⁺ are notoriously difficult to synthesize, especially as crystals large enough to be suitable for characterization of the structure or properties. It is now shown that the co‐existence of In³⁺ and Cr³⁺ induces a rapid crystal growth of large single crystals of heterometallic In‐Cr‐MOPs with the [M₈L₁₂] (M=In/Cr, L=dinegative 4,5‐imidazole‐dicarboxylate) cubane‐like structure. With a high concentration of protons from 12 carboxyl groups decorating every edge of the cube and an extensive H‐bonded network between cubes and surrounding H₂O molecules, the newly synthesized In‐Cr‐MOPs exhibit an exceptionally high proton conductivity (up to 5.8×10^?2 S cm^?1 at 22.5 °C and 98 % relative humidity, single crystal).     

Computational Insights into the Charge Relaying Properties of β‐Turn Peptides in Protein Charge Transfers

Density functional theory calculations suggest that β‐turn peptide segments can act as a novel dual‐relay elements to facilitate long‐range charge hopping transport in proteins, with the N terminus relaying electron hopping transfer and the C terminus relaying hole hopping migration. The electron‐ or hole‐binding ability of such a β‐turn is subject to the conformations of oligopeptides and lengths of its linking strands. On the one hand, strand extension at the C‐terminal end of a β‐turn considerably enhances the electron‐binding of the β‐turn N terminus, due to its unique electropositivity in the macro‐dipole, but does not enhance hole‐forming of the β‐turn C terminus because of competition from other sites within the β‐strand. On the other hand, strand extension at the N terminal end of the β‐turn greatly enhances hole‐binding of the β‐turn C terminus, due to its distinct electronegativity in the macro‐dipole, but does not considerably enhance electron‐binding ability of the N terminus because of the shared responsibility of other sites in the β‐strand. Thus, in the β‐hairpin structures, electron‐ or hole‐binding abilities of both termini of the β‐turn motif degenerate compared with those of the two hook structures, due to the decreased macro‐dipole polarity caused by the extending the two terminal strands. In general, the high polarity of a macro‐dipole always plays a principal role in determining charge‐relay properties through modifying the components and energies of the highest occupied and lowest unoccupied molecular orbitals of the β‐turn motif, whereas local dipoles with low polarity only play a cooperative assisting role. Further exploration is needed to identify other factors that influence relay properties in these protein motifs.     

Resistance characterizations of equiarboreal graphs

A weighted (unweighted) graph $G$ is called equiarboreal if the sum of weights (the number) of spanning trees containing a given edge in $G$ is independent of the choice of edge. In this paper, we give some resistance characterizations of equiarboreal weighted and unweighted graphs, and obtain the necessary and sufficient conditions for $k$-subdivision graphs, iterated double graphs, line graphs of regular graphs and duals of planar graphs to be equiarboreal. Applying these results, we obtain new infinite families of equiarboreal graphs, including iterated double graphs of 1-walk-regular graphs, line graphs of triangle-free 2-walk-regular graphs, and duals of equiarboreal planar graphs.     

Backbone coloring for triangle-free planar graphs

Acta Mathematicae Applicatae Sinica, English Series - Let G be a graph and H a subgraph of G. A backbone-k-coloring of (G, H) is a mapping f: V(G) → {1, 2, ···, k} such that...     

Transport with a Very Low Density Contrast in Hele–Shaw Cell and Porous Medium: Evolution of the Mixing Zone

The optimal concentration of a blue dye solution with 'tracer' properties, enabling a pollutant to be marked was determined by the use of numerical, theoretical and experimental approaches. Experimental investigations were performed on a transparent Hele–Shaw cell and the concentration distribution was analyzed using an optical technique based on dye light absorption properties. The injected optimal concentration was established thanks to a theoretical and experimental study carried out on the output signal dynamics. Using the same experimental conditions, numerical simulations were performed. The very good agreement between the data (experimental and numerical) clarified that: (i) the choice of the blue dye optimal concentration was valid and (ii) the concentration-dependent density should not be neglected in flow and transport equations even if it concerns a so-called 'tracer'. Following this remark, a theoretical aspect was developed in order to determine the analogous conditions between a Hele–Shaw cell and a porous medium for the variable density transport phenomenon. The structure of the concentration-dependent dispersion tensor used in the numerical code was obtained by homogenizing the Stokes flow of a bi-component mixture. The numerical results show that, as long as the tracer density does not exceed a certain value, it is not necessary to take into account a density contrast in terms of the dispersion tensor. The classical form of the Taylor dispersion tensor can be used successfully.     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).