Abstract. We consider a billiard in the punctured torus obtained by removing a small disk of radius ε > 0 from the flat torus T, with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity ω only. Let τ̃ε(ω), and respectively R̃ε(ω), denote the first exit time (length of the trajectory), and respectively the number of collisions wit...

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains’ penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high graftin...

A quantum Markovian activated atom-surface diffusion model with interacting adsorbates is proposed for the intermediate scattering function, which is shown to be complex-valued and factorizable into a classical-like and a quantum-mechanical factor. Applications to the diffusion of Na atoms on flat (weakly corrugated) and corrugated-Cu(001) surfaces at different coverages and surface temperature...

We consider variational problems defined on domains ‘weakly’ connected through a separation hyperplane (‘sieve plane’) by an ε-periodically distributed ‘contact zone’. We study the asymptotic behaviour as ε tends to 0 of integral functionals in such domains in the nonlinear and vector-valued case, showing that the asymptotic memory of the sieve is described by a nonlinear ‘capacitarytype’ formu...

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the dr...

We present a theoretical study of the dispersion relation of surface-plasmon resonances of mesoscopic metal-dielectric-metal microspheres. By analyzing the solutions to Maxwell's equations, we obtain a simple geometric condition for which the system exhibits a band of surface-plasmon modes whose resonant frequencies are weakly dependent on the multipole number. Using a modified Mie calculation,...

The phenomena resulting from interaction between polymers and membranes pose important problems for biological applications. Based on a scaling theory, we investigate the spontaneous curvature of a membrane induced by either flexible or semiflexible chain adsorption. Irrespective of chain stiffness, a weakly adsorbed polymer induces the membrane to bend away (to have a positive curvature) from ...

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...

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