New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems

We present an approach based on comparison principles for energy and interpolation properties to derive lower energy estimates for nonlinearly either locally damped or boundary damped vibrating systems. We show how the dissipation relation provides strong information on the asymptotic behavior of the energy of solutions. The geometrical situations are either one-dimensional, or radial two-dimensional or three-dimensional for annulus domains. We also consider the case of general domains, but in this case, for solutions with bounded velocities in time and space. In all these cases, the nonlinear damping function is assumed to have arbitrary (strictly sublinear) growth at the origin. We give results for strong solutions and stronger lower estimates for smoother solutions. The results are presented in two forms, either on the side of energy comparison principles, or through time-pointwise lower estimates. Under additional geometric assumptions, we give the resulting lower and upper estimates for four representative examples of damping functions. We further give a “weak” lower estimate (in the sense of a certain lim supt→∞) and an upper estimate of the velocity for smoother solutions in case of general damping functions and for radial, as well as multi-dimensional domains. We also discuss these estimates in the framework of optimality, which is not proved here, and indicate open problems raised by these results.     

On a coupled nonlinear singular thermoelastic system

For a coupled nonlinear singular system of thermoelasticity with one space dimension, we consider its initial boundary value problem on an interval. For one of the unknowns a classical condition is replaced by a nonlocal constraint of integral type. Because of the presence of a memory term in one of the equations and the presence of a weighted boundary integral condition, the solution requires a delicate set of techniques. We first solve a particular case of the given nonlinear problem by using a functional analysis approach. On the basis of the results obtained and an iteration method we establish the well-posedness of solutions in weighted Sobolev spaces.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.     

Reactivity of carbon monoxide towards high valent molybdenum complexes

Reaction of carbon monoxide (3 atm) with Mo(O)₂(mes)₂ (mes = MESITYL = C₆H₂Me₃-2,4,6) in pyridine at room temperature affords dimesityl ketone 1 (5%) and 1,1′-bis(mesitoyl)-1,1′,4,4′-tetrahydro-4,4′-bipyridine 2 (25%), the molecular structure of which has been determined by an X-ray diffraction study. The formation of 2 represents the first example of N-acylation of a pyridine by CO mediated by a transition metal complex. It has been shown that the relative ratio of 1 and 2 is dependent on the reaction conditions and that the presence of pyridine is essential for the formation of 1. Reactions of CO with the isoelectronic complex Mo(N^tBu)₂mes₂ contrast sharply with Mo(O)₂mes₂ and, under the same conditions, no dihydropyridine is formed, the sole identified products being 1 (60%) and mesityltertiobutyl amide HN(^tBu)COmes (40%). In light of the experimental results and of extended Hückel calculations on dioxo and diimido d⁰ molybdenum complexes, a tentative mechanism for the formation of 2 is proposed which involves oxycarbene-like intermediates in the case of the more electrophilic dioxo molybdenum species.     

Host-guest inclusion complex between β-cyclodextrin and paeonol: A theoretical approach

Host-guest interactions of β-cyclodextrin (β-CD) with paeonol (PAE) were simulated using semi-empirical PM3 and both ONIOM2 [(B3LYP/6-31G*:PM3), (HF/6-31G*:PM3)] methods. The results obtained with PM3 method clearly indicate that the complexes formed are energetically favored with or without solvent, the model 1 (PAE entering into the cavity of β-CD from its wide side by OCH3 group) is found more favored than the model 2 (PAE entering into the cavity of β-CD from its wide side by COCH3 group). Finally, natural bonding orbital (NBO) analysis was performed based on ONIOM2 optimized complexes to quantify the donor–acceptor interactions between PAE and β-CD.     

Mechanism of inclusion chaining in SmC* free-standing films

The self-assembly of colloidal inclusions has recently been shown in smectic C* freely suspended films. In such 2D systems, the organization of the inclusions is qualitatively explained by elastic interactions induced by the disruption of the orientational order in the SmC* host phase. The interaction between resulting inclusion-defect pairs exhibits a dipolar character. We have developed a simplified model representing every inclusion and its companion hyperbolic defect by (+1)- and (-1)-wedge disclination lines, respectively. A finite anchoring energy has been introduced to explain the coalescence of the thinnest inclusions. Our model enables us to explain the chaining of the thickest inclusions and confirms the inclusion size dependence on the stability of the chains.     

Decay estimates for second order evolution equations with memory

This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t→+∞. Our approach is based on integral inequalities and multiplier techniques.These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system.     

A DFT study of inclusion complexes of the antituberculosis drugs pyrazinamide and isoniazid with cucurbit[7]uril

A photoactive system, (2E)-3-{3-[(Z)-naphthalen-1-yldiazenyl] phenyl} prop-2-enoic acid, was synthesized and incorporated on to beta-cyclodextrin (β-CD) core through esterification of the hydroxyl groups of β-CD with the free carboxyl moiety of the chromophoric system by DCC coupling. The silver nanoparticle was synthesized by the reduction reaction executed on silver acetate in presence of dodecyl amine. The silver nano particles were dispersed in β-CD aggregates modified with photoactive system by phase transfer mechanism. The products were characterized by elemental analysis, melting point determination, UV–visible, FT-IR and NMR (¹H and ¹³C) spectral methods and SEM and TGA-DTG thermal studies. The thermal studies shows that the silver nanoparticle dispersed functionally modified beta cyclodextrin exhibited enhanced thermal stability compared to the functionalised β-CD.