Nonlinear response of SDOF systems under combined deterministic and random excitations

Dynamical systems subjected to random excitations exhibit non-linear behavior for sufficiently large motion. The multiple time scale method has been extensively utilized in the framework of non-linear deterministic analysis to obtain two averaged first-order differential equations describing the slow time scale modulation of amplitude and phase response. In this paper the multiple time scale method, opportunely modified to take properly into account the correlation structure of the stochastic input process, is adopted to derive a stochastic frequency-response relationship involving the response amplitude statistics and the input power spectral density. A low-intensity noise is assumed to separate the strong mean motion from its weak fluctuations. The moment differential equations of phase and amplitude are derived and a linearization technique applied to evaluate the second order statistics. The theory is validated through digital simulations on a nonlinear single degree of freedom model for the transversal oscillation of a cantilever beam with tip force and to a Duffing-Rayleigh oscillator, to analyze non-linear damping effects.     

Inverse compton scattering on laser beam and monochromatic isotropic radiation

Most of the known literature on inverse compton scattering (ICS) is based on earliest theoretical attempts and later approximations led by F.C. Jones and J.B. Blumenthal. We found an independent and more general analytical procedure which provide both relativistic and ultrarelativistic limits for ICS. These new analytical expressions can be derived in a straightforward way and they contain the previously reminded Jones’ results. Our detailed solutions may be probed by already existing as well future ICS experiments.     

A FPTAS for a class of linear multiplicative problems

In this paper we consider the problem of minimizing the product of two affine functions over a polyhedral set. An approximation algorithm is proposed and it is proved that it is a Fully Polynomial Time Approximation Scheme. We will also present and computationally investigate an exact version of the algorithm.     

Cross‐linked resins functionalized with triorganotin carboxylates: synthesis,characterization and preliminary catalytic screening in transesterification

Cross‐linked polymers containing triorganotin carboxylate functionalities were synthesized from ionic exchange resins bearing carboxylic groups. The organic tin substituents selected were methyl and butyl in order to ensure different accessibility at the metal centre. The functionalization degree depends on the different substituents and strongly affects the thermal stability of the final product. Catalytic screenings were performed in order to assess the activity of the above resins in transesterification reactions, using ethyl acetate as a substrate, together with differently hindered alcohols. The results obtained point to a negligible role of the bulkiness of tin substituents with a small contribution of the metal atom Lewis acidity in the conversion of the primary alcohol, whereas with secondary and tertiary alcohols the steric hindrance of the reagent strongly affects the conversion of the reacting alcohol. The transesterification process takes place at the liquid–solid interface, so that the catalyst grafted to an insoluble solid support can be completely removed by simple filtration. Copyright © 2005 John Wiley & Sons, Ltd.     

A practical entry to C18-constrained-E-ring analogues of methyllycaconitine (MLA): a concise new stereoselective approach to 8-oxa-decahydroisoquinolines accompanied by a simple microwaves-assisted synthesis of the succinimidobenzoate appendage of MLA

A Mannich-type intramolecular cyclization afforded access to a 8-oxa-decahydroisoquinoline heterocyclic system. Good stereoselectivity was observed. A promising microwave-assisted synthesis of the methylsuccinimidobenzoate moiety of methyllycaconitine has also been carried out.     

Synthesis and characterization of new polystyrenes containing tributyltin moieties linked to the aromatic ring through a methylenic spacer

Novel polymeric derivatives bearing tributyltin carboxylate moieties in the side chain were synthesized. The coordination at tin in solution and in the solid state was investigated by both Sn‐NMR and FT‐IR: the metal atom appears completely tetracoordinated in chloroform solution, while in the solid state all polymeric products exhibit both tetra‐ and pentacoordination at tin, the latter increasing with the amount of tin containing units. No evidence of tin leaching by hydrolysis of the organometallic ester was observed for these materials. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5372–5383, 2004     

Homogenization limit for electrical conduction in biological tissues in the radio-frequency rangeLimite d'homogénéisation pour la conduction électrique dans les tissus biologiques dans le domaine des radiofréquences

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u₀ of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation $\text{?}\text{div}\text{(σ}{}_0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+A}{}^0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+∫}{}_0{}^{\mathrm{t}}\text{A}{}^1\text{(t?τ)?}{}_{\mathrm{x}}\text{u}{}_0\text{(x,τ)}\text{d}\text{τ?}\text{F}\text{(x,t))=0}$ where σ₀>0 and the matrices A⁰, A¹ depend on geometric and material properties, while the vector function $\text{F}$ keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type. To cite this article: M. Amar et al., C. R. Mecanique 331 (2003).     

Minimum weight limit design under uncertainty

Summary The problem of probabilistic minimum weight limit design is formulated as a stochastic programming problem. The theoretical treatment considers monodimensional structures, geometrical parameters and integer design variables. An algorithm is proposed and illustrated for the case of pin-jointed structures with two random continuous variables. The paper follows previous researches of the Authors in the field of probabilistic approach to structural safety [29 ÷ 33].

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Sommario Il problema della progettazione a rottura per minimo peso su basi probabilistiche viene formulato quale problema di programmazione stocastica. La trattazione teorica si estende alle strutture monodimensionali, comprende variabili di tipo geometrico nonchè variabili intere: l'algoritmo proposto ed illustrato per la risoluzione numerica riguarda le strutture reticolari interessate da due variabili casuali continue. Il lavoro fa seguito a precedenti ricerche degli scriventi in tema di concezione probabilistica della sicurezza [29 ÷ 33].

     

Surface Modification with Control over Ligand Density for the Study of Multivalent Biological Systems

In the study of multivalent interactions at interfaces, as occur for example at cell membranes, the density of the ligands or receptors displayed at the interface plays a pivotal role, affecting both the overall binding affinities and the valencies involved in the interactions. In order to control the ligand density at the interface, several approaches have been developed, and they concern the functionalization of a wide range of materials. Here, different methods employed in the modification of surfaces with controlled densities of ligands are being reviewed. Examples of such methods encompass the formation of self-assembled monolayers (SAMs), supported lipid bilayers (SLBs) and polymeric layers on surfaces. Particular emphasis is given to the methods employed in the study of different types of multivalent biological interactions occurring at the functionalized surfaces and their working principles.