Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

A stable second‐order mass‐weighted upwind scheme for unstructured meshes

In this paper, an original second‐order upwind scheme for convection terms is described and implemented in the context of a Control‐Volume Finite‐Element Method (CVFEM). The proposed scheme is a second‐order extension of the first‐order MAss‐Weighted upwind (MAW) scheme proposed by Saabas and Baliga (Numer. Heat Transfer 1994; 26B :381–407). The proposed second‐order scheme inherits the well‐known stability characteristics of the MAW scheme, but exhibits less artificial viscosity and ensures much higher accuracy. Consequently, and in contrast with nearly all second‐order upwind schemes available in the literature, the proposed second‐order MAW scheme does not need limiters. Some test cases including two pure convection problems, the driven cavity and steady and unsteady flows over a circular cylinder, have been undertaken successfully to validate the new scheme. The verification tests show that the proposed scheme exhibits a low level of artificial viscosity in the pure convection problems; exhibits second‐order accuracy for the driven cavity; gives accurate reattachment lengths for low‐Reynolds steady flow over a circular cylinder; and gives constant‐amplitude vortex shedding for the case of high‐Reynolds unsteady flow over a circular cylinder. Copyright © 2005 John Wiley & Sons, Ltd.     

High-field EPR Study of the Effect of Chloride on Mn2+ Ions in Frozen Aqueous Solutions

The effect of chloride concentration on Mn²⁺ (S = 5/2, I = 5/2) ions in frozen aqueous solutions is studied by high-field high-frequency electron paramagnetic resonance (HFEPR). The usually six sharp lines characteristic of Mn²⁺ ions, arising from the m _s  = ?1/2 → 1/2 transition, is modified by the addition of Cl^? anions and the six resonances become much broader and more complex. This new feature likely arises from the ligation of one Cl^? anion to a hydrated Mn²⁺ ion forming a [Mn(H₂O)₅Cl]^? complex. This complex increases linearly with Cl^? concentration with an association constant of K _{a, apparent} = 61 M^?1. The structure of the putative chloride complex was studied using density functional theory calculations and the expected zero-field interaction of such a manganese center was calculated using the superposition model. The predicted values were similar to those determined from the simulation of the spectrum of the m _s  = ?5/3 → ?3/2 transition of the chloride complex. This effect of Cl^? anions occurs at biologically relevant concentration and can be used to probe the Mn²⁺ ions in cellular and protein environments.     

Multiple Unbounded Positive Solutions for Three-Point BVPs with Sign-Changing Nonlinearities on the Positive Half-Line

This work is concerned with the existence of unbounded positive solutions for a second-order nonlinear three-point boundary value problem on the positive half-line. The interesting points of the results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using recent fixed point theorems on cones in a special Banach space.     

Buckling of a stiff film bound to a compliant substrate—Part I:: Formulation, linear stability of cylindrical patterns, secondary bifurcations

The buckling of a thin elastic film bound to a compliant substrate is studied: we analyze the different patterns that arise as a function of the biaxial residual compressive stress in the film. We first clarify the boundary conditions to be used at the interface between film and substrate. We carry out the linear stability analysis of the classical pattern made of straight stripes, and point out secondary instabilities leading to the formation of undulating stripes, varicose, checkerboard or hexagonal patterns. Straight stripes are found to be stable in a narrow window of load parameters only. We present a weakly nonlinear post-buckling analysis of these patterns: for equi-biaxial residual compression, straight wrinkles are never stable and square checkerboard patterns are found to be optimal just above threshold; for anisotropic residual compression, straight wrinkles are present above a primary threshold and soon become unstable with respect to undulating stripes. These results account for many of the previously published experimental or numerical results on this geometry.     

Polynitrile anions as ligands: From magnetic polymeric architectures to spin crossover materials

The use of polynitrile anions as ligands (L) either alone or in combination with neutral co-ligands (L′) is a very promising and appealing strategy to get molecular architectures with different topologies and dimensionalities thanks to their ability to coordinate and bridge metal ions in many different ways. The presence of several potentially coordinating nitrile groups (or even other donor groups as –OH, –SH or –NH₂), their rigidity and their electronic delocalization allow the synthesis of original magnetic high dimensional coordination polymers with transition metals ions. Furthermore, these ligands have shown coordinating and bridging capabilities in novel discrete and polymeric bistable materials (materials showing original magnetic behaviours or spin crossover (SCO) transitions). Here we report an overview of the results obtained with some of these modified polynitrile ligands, showing their rich coordination chemistry and their crucial role in new molecular materials exhibiting unusual magnetic transitions.     

A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository

We prove existence of solutions for a new model of two compressible and partially miscible phase flow in porous media, applied to gas migration in an underground nuclear waste repository. This model, modeling fully and partially water saturated situations, consist of a coupled system of quasilinear parabolic partial differential equations. We seek a new set of variables in order to obtain a system which belongs to the class of equations considered by Alt and Luckhaus such that it would be possible to use their existence theorem. A simulation of a numerical test case is performed in order to numerically demonstrate the ability of this model to take in account the appearance of one phase. To cite this article: F. Smaï, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Positive Solutions for Singular BVPs with Sign Changing and Derivative Depending Nonlinearity on the Positive Half-Line

This work is devoted to the existence of positive, vanishing nontrivial solutions for singular boundary value problems on the half-line. The nonlinearity, which encompasses some physical laws, depends on the solution and its derivative, may exhibit a singularity at the origin in its second argument and is further allowed to change sign. Existence results are proved using two different methods: the upper and lower solutions technique and the fixed point index on cones of weighted Banach spaces. The singularity is treated by means of regularization, approximation and compactness arguments. The problem originates from chemistry and biology.     

Asymmetric azido-copper(II) bridges: ferro- or antiferromagnetic? experimental and theoretical magneto-structural studies

Reaction of NaN(3) with the [Cu(II)(tn)](2+) ion (tn = 1,3-diaminopropane) in basic aqueous solution yields the azido-bridged complex of formula [Cu(2)(tn)(2)(N(3))(4)] (1), which is characterized by X-ray crystallography. The structure of 1 is made up of dinuclear neutral complexes, of formula [Cu(2)(tn)(2)(N(3))(4)], resulting from the assembling of two mononuclear units through two equivalent end-on azide bridges connecting asymmetrically two Cu(tn)(N(3))(2) entities. These dinuclear units are connected through two asymmetric end-to-end N(3) bridges to form a chain of dimers. Magnetic measurements for compound 1 show weak antiferromagnetic exchange interactions between the Cu(II) ions. The magnetic data were modeled using the susceptibility expression derived for an alternating AF S = 1/2 chain. A very satisfactory fit over the whole temperature range was obtained with g = 2.1438(4), J(1) = -3.71(2) cm(-1), and J(2) = -3.10(2) cm(-1) (J(1) and J(2) are the singlet-triplet separations). This magnetic behavior differs from those observed for similar examples which were reported as having alternating ferro- and antiferromagnetic exchange interactions; thus, DFT calculations were done to understand the nature of the magnetic coupling in such asymmetric end-on and end-to-end N(3) bridges. Theoretical results show that the double asymmetric end-on bridges produce antiferromagnetic coupling while the end-to-end ones can present ferro- or antiferromagnetic coupling depending on the copper coordination sphere.     

Existence Results for Singular Boundary Value Problems on Unbounded Domains in Banach Spaces

In this paper, the Krasnosels’kii fixed point theorem in cones for strict set-contractions is used to investigate the existence of single and twin positive solutions for a class of a two-point boundary value problem of second-order nonlinear differential equations posed on an infinite interval. The nonlinearity, which may have a time-singularity, takes values in a general Banach space and has at most polynomial growth with respect to the unknown.