Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

Nanoscale electrical conductivity of the purple membrane monolayer

Nanoscale electron transport through the purple membrane monolayer, a two-dimensional crystal lattice of the transmembrane protein bacteriorhodopsin, is studied by conductive atomic force microscopy. We demonstrate that the purple membrane exhibits nonresonant tunneling transport, with two characteristic tunneling regimes depending on the applied voltage (direct and Fowler-Nordheim). Our results show that the purple membrane can carry significant current density at the nanometer scale, several orders of magnitude larger than previously estimated by macroscale measurements.

Heat pulse line-source method to determine thermal conductivity of consolidated rocks

An instrument designed to measure thermal conductivity of consolidated rocks, dry or saturated, using a transient method is presented. The instrument measures relative values of the thermal conductivity, and it needs calibration to obtain absolute values. The device can be used as heat pulse line source and as continuous heat line source. Two parameters to determine thermal conductivity are proposed: TMAX, in heat pulse line source, and SLOPE, in continuous heat line source. Its performance is better, and the operation simpler, in heat pulse line-source mode with a measuring time of 170 s and a reproducibility better than 2.5%. The sample preparation is very simple on both modes. The performance has been tested with a set of ten rocks with thermal conductivity values between 1.4 and 5.2 W m¿1 K¿1 which covers the usual range for consolidated rocks.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Practical algorithms for a family of waterfilling solutions

Many engineering problems that can be formulatedas constrained optimization problems result in solutionsgiven by a waterfilling structure; the classical example is thecapacity-achieving solution for a frequency-selective channel.For simple waterfilling solutions with a single waterlevel and asingle constraint (typically, a power constraint), some algorithmshave been proposed in the literature to compute the solutionsnumerically. However, some other optimization problems result insignificantly more complicated waterfilling solutions that includemultiple waterlevels and multiple constraints. For such cases, itmay still be possible to obtain practical algorithms to evaluate thesolutions numerically but only after a painstaking inspection ofthe specific waterfilling structure. In addition, a unified view ofthe different types of waterfilling solutions and the correspondingpractical algorithms is missing.The purpose of this paper is twofold. On the one hand, itoverviews the waterfilling results existing in the literature from aunified viewpoint. On the other hand, it bridges the gap betweena wide family of waterfilling solutions and their efficient implementationin practice; to be more precise, it provides a practicalalgorithm to evaluate numerically a general waterfilling solution,which includes the currently existing waterfilling solutions andothers that may possibly appear in future problems.