A residual-based a posteriori error estimator for a two-dimensional fluid–solid interaction problem

In this paper, we develop an a posteriori error analysis of a mixed finite element method for a fluid–solid interaction problem posed in the plane. The media are governed by the acoustic and elastodynamic equations in time-harmonic regime, respectively, and the transmission conditions are given by the equilibrium of forces and the equality of the normal displacements of the solid and the fluid. The coupling of primal and dual-mixed finite element methods is applied to compute both the pressure of the scattered wave in the linearized fluid and the elastic vibrations that take place in the elastic body. The finite element subspaces consider continuous piecewise linear elements for the pressure and a Lagrange multiplier defined on the interface, and PEERS for the stress and rotation in the solid domain. We derive a reliable and efficient residual-based a posteriori error estimator for this coupled problem. Suitable auxiliary problems, the continuous inf-sup conditions satisfied by the bilinear forms involved, a discrete Helmholtz decomposition, and the local approximation properties of the Clément interpolant and Raviart–Thomas operator are the main tools for proving the reliability of the estimator. Then, Helmholtz decomposition, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are employed to show the efficiency. Finally, some numerical results confirming the reliability and efficiency of the estimator are reported.     

Geometrizing Relativistic Quantum Mechanics

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.     

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.     

Non-fouling microfluidic chip produced by radio frequency tetraglyme plasma deposition

This Technical Note presents the direct surface modification of a glass/PTFE hybrid microfluidic chip, via radio frequency glow discharge plasma polymerisation of tetraethlylene glycol dimethylether (tetraglyme), to produce hydrophilic, non-fouling, PEO-like surfaces. We use several techniques including X-ray photoelectron spectroscopy (XPS), direct enzyme-linked immunosorbent assays (ELISA) and immunofluorescent imaging to investigate the channel coatings. Our results indicate the successful deposition of a PEO-like coating onto microchannel surfaces that has both solution and shelf stability (>3 months) and is capable of preventing fibrinogen adsorption to the microchannel surfaces.     

Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional framework structures: isomorphous bis(2,6‐diamino‐3,5‐dibromopyridinium) tetrabromidometallate(II) salts with CdII and MnII

In the structural motifs of two isomorphous triclinic salts, (C₅H₆Br₂N₃)₂[MBr₄] (M = Cd^II and Mn^II), each [MBr₄]²⁻ anion interacts with eight surrounding 2,6‐diamino‐3,5‐dibromopyridinium cations through intermolecular C/N—H...Br and Br...Br interactions, leading to a three‐dimensional framework structure. The cations show a minor degree of π–π stacking, adding extra stability to the three‐dimensional architecture.     

Three isomorphous 2,6‐dibromopyridinium tetrabromidometallates: (C5H4Br2N)2[MBr4]·2H2O (M = Cu,Cd and Hg)

The structures of three isomorphous compounds, namely bis(2,6‐dibromopyridinium) tetrabromidocuprate(II) dihydrate, (C₅H₄Br₂N)₂[CuBr₄]·2H₂O, bis(2,6‐dibromopyridinium) tetrabromidocadmate(II) dihydrate, (C₅H₄Br₂N)₂[CdBr₄]·2H₂O, and bis(2,6‐dibromopyridinium) tetrabromidomercurate(II) dihydrate, (C₅H₄Br₂N)₂[HgBr₄]·2H₂O, show a crystal supramolecularity represented by M—Br...H—O—H...Br—M intermolecular interactions along with (π)N—H...OH₂ hydrogen‐bonding interactions forming layers connected via aryl–aryl face‐to‐face stacking of cations, leading to a three‐dimensional network. The anions have significantly distorted tetrahedral geometry and crystallographic C₂ symmetry. The stability of this crystal lattice is evidenced by the crystallization of a whole series of isomorphous compounds.     

General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping

In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ρ₁, ρ₂, k₁, k₂ and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear damped Timoshenko systems with second sound—Global existence and exponential stability

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd.     

Uniform decay in a Timoshenko-type system with past history

Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system

ρ₁φ_tt−K(φ_x+ψ)_x=0,