The motion of a solid with large deformations

We study the motion of a solid with large deformations. The solid may be loaded on its surface by needles, rods, beams, plates… Therefore it is wise to choose a third-gradient theory for the body. Stretch matrix of the polar decomposition has to be symmetric. This is an internal constraint which introduces a reaction stress in the Piola–Kirchhoff–Boussinesq stress. We prove that there exists a motion that satisfies the complete equations of Mechanics in a convenient variational framework. This motion is local-in-time because it may be interrupted by crushing, resulting in a discontinuity of velocity with respect to time, i.e., an internal collision.     

The Allen–Cahn equation with dynamic boundary conditions and mass constraints

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd.     

$$\pi $$π-Formulas and Gray code

In previous papers we introduced a class of polynomials which follow the same recursive formula as the Lucas–Lehmer numbers, studying the distribution of their zeros and remarking that this distribution follows a sequence related to the binary Gray code. It allowed us to give an order for all the zeros of every polynomial \(L_n\). In this paper, the zeros, expressed in terms of nested radicals, are used to obtain two formulas for \(\pi \): the first can be seen as a generalization of the known formula

$$\begin{aligned} \pi =\lim _{n\rightarrow \infty } 2^{n+1}\cdot \sqrt{2-\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{n}}, \end{aligned}$$

related to the smallest positive zero of \(L_n\); the second is an exact formula for \(\pi \) achieved thanks to some identities valid for \(L_n\).

     

Ab initio calculation of some low-lying electronic excited states of methane

The energies of some low-lying electronic excited states of methane are calculated by using wave functions built up in terms of plane waves modulated by multicenter Gaussian factors. The wave functions of the various states are evaluated by a two steps iterative process. In the first step, each excited orbital is determined while keeping all other rigid; in the second, rearrangement effects are introduced. Final results are in good agreement with experimental data and allow to enhance an assignement hypothesis for the first electronic transitions.     

Kinetic study on effect of novel cationic dimeric surfactants for the cleavage of carboxylate ester

Kinetic study has been performed to understand the reactivity of novel cationic gemini surfactants viz. alkanediyl‐α,ω‐bis(hydroxyethylmethylhexadecylammonium bromide) C₁₆‐s‐C₁₆ MEA, 2Br^? (where s = 4, 6) in the cleavage of p‐nitrophenyl benzoate (PNPB). Novel cationic gemini C₁₆‐s‐C₁₆ MEA, 2Br^? surfactants are efficient in promoting PNPB cleavage in presence of butane 2,3‐dione monoximate and N‐phenylbenzohydroxamate ions. Model calculation revealed that the higher catalytic effect of ethanol moiety of gemini surfactants (C₁₆H₃₃N⁺ C₂H₄OH CH₃ (CH₂)_S N⁺ C₂H₄OH CH₃C₁₆H₃₃, 2Br^?, s = 4, 6) is due to their higher binding capacity toward substrate. This is in line with finding that binding constants for novel series of cationic gemini surfactants are higher than conventional cationic gemini (C₁₆H₃₃N⁺(CH₃)₂(CH₂)_SN⁺(CH₃)₂C₁₆H₃₃, 2Br^?, s = 10, 12), cetyldimethylethanolammonium bromide and zwitterionic surfactants, i.e. C_nH_2n+1N⁺Me₂ (CH₂)₃ SO₃^? (n = 10; SB3‐10). The fitting of kinetic data was analyzed by the pseudophase model. Copyright © 2013 John Wiley & Sons, Ltd.     

Glass transition temperatures of some linear polymers containing phenyl side groups

The glass transition temperatures of a number of poly(vinyl phenyl ketones), poly-(vinyl benzoates), and poly(phenyl acrylates) have been measured by a refractometric method. The effects exerted on T_g by the nature and position of the ring substituents and by the different groups binding the pendant phenyl rings to the polyvinyl chain are discussed. The importance of knowledge of the side-group motions in the glassy state for the interpretation of glass temperature data is emphasized.     

Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems

Numerical Algorithms - Recently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods...     

On the metabolites produced by Colletotrichum gloeosporioides a fungus proposed for the Ambrosia artemisiifolia biocontrol; spectroscopic data and absolute configuration assignment of colletochlorin A

Ambrosia artemisiifolia L. is responsible for serious allergies induced on humans. Different approaches for its control were proposed during the COST Action FA1203 “Sustainable management of Ambrosia artemisiifolia in Europe” (SMARTER). Fungal secondary metabolites often show potential herbicidal activity. Three phytotoxins were purified from the fungal culture filtrates of Colletotrichum gloeosporioides, isolated from infected leaves of A. artemisiifolia. They were identified by spectroscopic and chemical methods as colletochlorin A, orcinol and tyrosol (1, 2 and 3). The absolute configuration 6’R to colletochlorin A was assigned for the first time applying the advanced Mosher’s method. When assayed by leaf-puncture on A. artemisiifolia only 1 caused the appearance of large necrosis. The same symptoms were also induced by 1 on ambrosia plantlets associated with plant wilting. On Lemna minor, colletochlorin A caused a clear fronds browning, with a total reduction in chlorophyll content.