Evidence for contact delocalization in atomic scale friction

We analyze an advanced two-spring model with an ultra-low effective tip mass to predict nontrivial and physically rich 'fine structure' in the atomic stick-slip motion in Friction Force Microscopy (FFM) experiments. We demonstrate that this fine structure is present in recent, puzzling experiments. This shows that the tip apex can be completely or partially delocalized, thus shedding new light on what is measured in FFM and, possibly, what can happen with the asperities that establish the contact between macroscopic sliding bodies.Comment: 4 pages text and 3 figure

The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Ana

Determination of the input filter parameters of the active rectifier with a fixed modulation frequency

Goal. Development of a methodology for calculating the parameters of the active rectifier-voltage source input filter operating with a fixed modulation frequency to ensure electromagnetic compatibility with the supply network acceptable by standards at minimum values of the input inductance and checking its main characteristics on a mathematical model. Methodology. The authors have developed a methodology for calculating the parameters of the input filter of an active rectifier-voltage source. The calculation results are verified on the constructed mathematical model of a frequency converter, the scheme of which is an active rectifier and an autonomous voltage inverter. A series of experiments was carried out on a mathematical model to study the dependence of the total harmonic distortion of current and mains voltage on the value of the input inductance for various parameters of the input filter. Results. The structure and calculation procedure the input filter of an active rectifier operating with a fixed modulation frequency are proposed. The simulation results showed that the inclusion of a filter at the input of the active rectifier significantly improves its electromagnetic compatibility with the supply network in the entire range of variation of the input inductance of the circuit and makes it possible to achieve the values of the total harmonic distortion permissible by the norms. Originality. A structure and a calculation procedure the input filter of an active rectifier-voltage source operating with a fixed modulation frequency are proposed. Practical significance. The dependencies obtained in the article allow us to evaluate the relationship between the parameters of the filter elements and its characteristics among themselves and come to a compromise between them when designing a scheme for specific technical conditions.В статті запропоновано структуру та методику розрахунку вхідного фільтру активного випрямляча-джерела напруги, який працює з фіксованою частотою модуляції. Отримані залежності дозволяють оцінити взаємозв'язок параметрів елементів фільтра та його характеристик між собою та дійти компромісу між ними під час проектування схеми для конкретних технічних умов. Результати моделювання показали, що включення додаткового ланцюга RC фільтра на вході активного випрямляча істотно покращує його електромагнітну сумісність з мережею живлення у всьому діапазоні зміни вхідної індуктивності схеми та дозволяє досягати допустимих нормами значень сумарного коефіцієнту гармонічних спотворень

Non-affine geometrization can lead to nonphysical instabilities

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geometrical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures: http://iopscience.iop.org/1751-8121/48/7/07510

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.Comment: 4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Let

A hierarchy of models related to nanoflows and surface diffusion

In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis