Asymptotic stability of finite energy in Navier Stokes-elastic wave interaction

We consider a model of fluid-structure interaction in a bounded domain Ω∈ℝ² where Ω is comprised of two open adjacent sub-domains occupied, respectively, by the solid and the fluid. This leads to a study of Navier Stokes equation coupled on the interface to the dynamic system of elasticity. The characteristic feature of this coupled model is that the resolvent is not compact and the energy function characterizing balance of the total energy is weakly degenerated. These combined with the lack of mechanical dissipation and intrinsic nonlinearity of the dynamics render the problem of asymptotic stability rather delicate. Indeed, the only source of dissipation is the viscosity effect propagated from the fluid via interface. It will be shown that under suitable geometric conditions imposed on the geometry of the interface, finite energy function associated with weak solutions converges to zero when the time t converges to infinity. The required geometric conditions result from the presence of the pressure acting upon the solid.     

Nonionic diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains: thermotropic and lyotropic liquid crystalline phase behaviour

The thermotropic and lyotropic liquid crystalline phase behaviour of a series of diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains (geranoyl, H-farnesoyl, and phytanoyl) has been investigated. When neat, both H-farnesoyl and phytanoyl diethanolamide form a smectic liquid crystalline structure at sub-zero temperatures. In addition, all three diethanolamides exhibit a glass transition temperature at around -73 °C. Geranoyl diethanolamide forms a lamellar crystalline phase with a lattice parameter of 17.4 ? following long term storage accompanied by the loss of the glass transition. In the presence of water, H-farnesoyl and phytanoyl diethanolamide form lyotropic liquid crystalline phases, whilst geranoyl diethanolamide forms an L(2) phase. H-farnesoyl diethanolamide forms a fluid lamellar phase (L(α)) at room temperature and up to ～ 40 °C. Phytanoyl diethanolamide displays a rich mesomorphism forming the inverse diamond (Q(II)(D)) and gyroid (Q(II)(G)) bicontinuous cubic phases in addition to an L(α) phase.     

Single dibenzoterrylene molecules in naphthalene and 2,3-dimethylnaphthalene crystals: vibronic spectra

Fluorescence excitation spectra of single dibenzoterrylene (DBT) molecules embedded in naphthalene (N) and 2,3-dimethylnaphthalene (2,3-DMN) crystals were studied at 5 K. The frequencies characterizing the vibronic structure of single DBT molecules in an N crystal agree with the theoretical prediction for the isolated DBT molecule. The 'dipolar' disorder encountered in 2,3-DMN crystals leads to a broad distribution of frequencies of the (0,0) lines of single DBT molecules. Moreover, the observed vibronic frequencies and intensities in the spectrum of DBT in 2,3-DMN crystals are slightly different to those in an N crystal. We conclude that the structure of DBT molecules in a 2,3-DMN crystal is disturbed in comparison with isolated DBT and the main change concerns its central tetracene moiety.     

Prototropy,Intramolecular Interactions,Electron Delocalization,and Physicochemical Properties of 1,8-dihydroxy-9-anthrone—DFT-D3 Study of Substituent Effects

1,8-dihydroxy-9-anthrone are tricyclic compounds with a ketone group in the middle ring and two hydroxyl groups substituted in the side-aromatic rings what results in formation of two intramolecular hydrogen bonds in which the oxygen atom from the ketone group is the proton acceptor. 1,8-dihydroxy-9-anthrones in which intramolecular proton transfer between C10 and CO in the middle ring occurs, can exist in a tautomeric keto-enol equilibrium. For anthralin, the most important representative of this group, this equilibrium has been studied previously, but it has not been studied for its derivatives. Substituents in the middle ring change the geometry of 1,8-dihydroxy-9-anthrones so they are also expected to affect the keto-enol equilibrium. It is also important to study the effect of intramolecular hydrogen bonds on the structure of both tautomeric forms. It was found that the nature of the substituent in the middle ring could affect the antioxidant properties of the investigated compound.     

Electrochemistry of Tetrathiafulvalene Ligands Assembled on the Surface of Gold Nanoparticles

The synthesis of a tetrathiafulvalene (TTF) derivative, S-[4-({4-[(2,2′-bi-1,3-dithiol-4-ylmethoxy)methyl] phenyl}ethynyl)phenyl] ethanethioate, suitable for the modification of gold nanoparticles (AuNPs), is described in this article. The TTF ligand was self-assembled on the AuNP surface through ligand exchange, starting from dodecanethiol-stabilized AuNPs. The resulting modified AuNPs were characterized by TEM, UV-Vis spectroscopy, and electrochemistry. The most suitable electrochemical method was the phase-sensitive AC voltammetry at very low frequencies of the sine-wave perturbation. The results indicate a diminishing electronic communication between the two equivalent redox centers of TTF and also intermolecular donor–acceptor interactions manifested by an additional oxidation wave upon attachment of the ligand to AuNPs.     

From finitary to infinitary second‐order logic

A back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second‐order languages with an infinite non‐logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second‐order languages whose non‐logical vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second‐order languages can be extended to the infinitary second‐order languages. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inertial Manifolds for von Karman Plate Equations

Inertial manifolds associated with nonlinear plate models governed by dynamical von Karman equations are considered. Three different dissipative mechanisms are discussed: viscous, structural and thermal damping. Though the systems considered are subject to some dissipation, the overall dynamics may not be dissipative. This means that the energy may not be decreasing. The main result of the paper establishes the existence of an inertial manifold subject to the spectral gap condition for linearized problems. The validity of the spectral gap condition depends on the geometry of the domain and the type of damping. It is shown that the spectral gap condition holds for plates of rectangular shape. In the case of viscous damping, which is associated with hyperbolic-like dynamics, it is also required that the damping parameter be sufficiently large. This last requirement is not needed for other types of dissipation considered in the paper.     

The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.     

Subcritical scattering from buried elastic shells

Buried objects have been largely undetectable by traditional high-frequency sonars due to their insignificant bottom penetration. Further, even a high grazing angle sonar approach is vastly limited by the coverage rate dictated by the finite water depth, making the detection and classification of buried objects using low frequency, subcritical sonar an interesting alternative. On the other hand, such a concept would require classification clues different from the traditional high-resolution imaging and shadows to maintain low false alarm rates. A potential alternative, even for buried targets, is classification based on the acoustic signatures of man-made elastic targets. However, the elastic responses of buried and proud targets are significantly different. The objective of this work is to identify, analyze, and explain some of the effects of the sediment and the proximity of the seabed interface on the scattering of sound from completely and partially buried elastic shells. The analysis was performed using focused array processing of data from the GOATS98 experiment carried out jointly by MIT and SACLANTCEN, and a new hybrid modeling capability combining a virtual source-or wave-field superposition-approach with an exact spectral integral representation of the Green's functions for a stratified ocean waveguide, incorporating all multiple scattering between the object and the seabed. Among the principal results is the demonstration of the significant role of structural circumferential waves in converting incident, evanescent waves into backscattered body waves, emanating to the receivers at supercritical grazing angles, in effect making the target appear closer to the sonar than predicted by traditional ray theory.