Modelling of Progressive Strain Tests by a Non-linear Relaxation Approach

A model based on the thermodynamics of relaxations of continuous media (called DNLR as Distribution of nonlinear relaxations) is used to describe the tension/torsion progressive strain phenomenon. The proposed model is compared to the experimental data obtained by Benham on mild steel at room temperature with satisfactory results. We discuss the capacities and the relevance of the model obtained.     

A fully Galerkin method for the damped generalized regularized long‐wave (DGRLW) equation

In this article, a fully discrete Galerkin scheme based on a nonlinear Crank–Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ? is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C _P ”[7], close to the second laser threshold “2C _2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.     

Magnetism in spin-coated pristine TiO2 thin films

Spin coated pristine TiO₂ thin films show magnetic behaviors that are similar to those of pulsed laser ablated TiO₂ thin films that were reported previously. It seems that in this kind of material, ferromagnetism (FM) is indeed intrinsic, and it can be achieved by various deposition techniques. The fact that oxygen annealing degrades the magnetic moment implies that the observed magnetism is likely due to defects or/and oxygen vacancies. Moreover, thick films that were deposited under the same growth conditions have the magnetic ordering degraded enormously. It is found that as for FM in undoped TiO₂ films made by the chemical solution deposition, not only do defects/oxygen vacancies play a role, but also the confinement effects seem to be important.     

Uniform Existence of the Integrated Density of States for Randomly Weighted Hamiltonians on Long-Range Percolation Graphs

We consider random Hamiltonians defined on long-range percolation graphs over $\mathbb {Z}^{d}$ . The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.     

Weak versus strong harmonic-expansion analyses of self-pulsing lasers: II—the inhomogeneously broadened system

A simple harmonic expansion method is applied to investigate some aspects of the dynamic properties of the integro-differential ‘Maxwell-Bloch’ equations that describe the self-pulsing regime of a single-mode inhomogeneously broadened laser. First, we show that the usual small perturbative methods only describe the transient relaxation oscillations, characteristic of the signal relaxing towards its permanent state, either stable or unstable. Second, we show that an adapted strong harmonic expansion analysis applied to the permanent pulsing solutions yields an accurate evaluation of the pulsing frequencies.     

Alpha and beta isomers of tetrahafnium(IV) containing decatungstosilicates, [Hf4(OH)6(CH3COO)2(x-SiW10O37)2]12- (x = α, β)

The two dimeric, Hf-containing tungstosilicates [Hf(4)(OH)(6)(CH(3)COO)(2)(α-SiW(10)O(37))(2)](12-) (1) and [Hf(4)(OH)(6)(CH(3)COO)(2)(β-SiW(10)O(37))(2)](12-) (2) have been synthesized by reacting HfCl(4) with [γ-SiW(10)O(36)](8-) in potassium acetate solutions at pH = 3.6 and 4.8, respectively. Polyanions 1 and 2 comprise a tetrahafnium(iv) assembly {Hf(4)(OH)(6)(CH(3)COO)(2)} sandwiched between two dilacunary [α-SiW(10)O(36)](8-) (in 1) or {β-SiW(10)} (in 2) Keggin type decatungstosilicates. This implies that the starting precursor {γ-SiW(10)} isomerizes in situ to [β-SiW(10)O(37)](10-) and then to [α-SiW(10)O(37)](10-) by controlled variation of pH and temperature. The hydrated potassium salts of 1 and 2 were investigated in the solid state by single-crystal XRD, FT-IR, thermogravimetric and elemental analyses, and in solution by UV-Vis and (183)W NMR spectroscopy, and electrochemistry.     

Mechanical reinforcement and water repellency induced to cellulose sheets by a polymer treatment

The present study reports a simple method to control the mechanical and surface properties of cellulose fiber networks and to protect them from humidity, without altering their initial morphology. This is achieved by dip coating the fiber networks in solutions containing different amounts of ethyl cyanoacrylate monomer (ECA). Under ambient humidity and due to the presence of the -OH groups of the cellulose, the ECA polymerizes around each individual cellulosic fiber forming a thin poly(ethyl cyanoacrylate) (PECA) shell. PECA was found to interact with the cellulose surface via hydrogen bonding as evidenced by Fourier transform infrared spectroscopy and thermogravimetric analysis measurements. The detailed surface characterization reveals that only 3.5 wt% of ECA in solution is sufficient to form compact PECA cladding around every cellulose fiber. After the proposed treatment the cellulose sheets become hydrophobic, well protected from the environmental humidity and with increased Young’s modulus.     

Molecular Imprints Frozen by Strong Intermolecular Interactions in Place of Cross-Linking

A new way to freeze molecular imprints in a polymer material is reported. So far, molecular imprinted polymers (MIP) involve copolymerization of a functional monomer and large amounts of cross-linking agent, which keeps the template shape memory in rigid molecular imprints. MIP materials are prepared herein without cross-linking agent. Stiff chains of polyaniline grafted on a solid support as a brush-like material achieve the necessary rigidity. Differential adsorption to imprinted and non-imprinted materials provides evidence of molecular imprints. A correct adsorption isotherm for mobile adsorbed layers (Volmer isotherm) is introduced instead of the popular but inadequate Langmuir isotherm. Non-selective adsorption is entropic, whereas adsorption to molecular imprints has an enthalpic contribution coming from specific interactions. Fast adsorption kinetics are a definite benefit with regards to applications such as chromatographic separations and chemical sensors.