Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations

We present a study of general symmetry properties of a Brownian ratchet model. The study is based both on constructing chains of symmetry transformations reflecting explicit and hidden symmetries of the average ratchet velocity as a functional of the spatially periodic potential energy of a nanoparticle and on taking into account the symmetry types of periodic functions that are components of the potential energy of an additive-multiplicative form. A ratchet with a sawtooth stationary potential profile, dichotomously perturbed by a spatially harmonic signal, is investigated. Conclusions are made on both the possibility of occurrence of the ratchet effect and its direction for given values of the asymmetry parameter of the sawtooth profile, phase shifts of the control component, and frequencies of temporal fluctuations. These conclusions have been obtained only on the basis of symmetry transformations; that demonstrates the predictive value of the approach presented. The results of the symmetry analysis are confirmed by numerical simulation of the functioning of a ratchet with dichotomous stochastic spatially periodic fluctuations of the nanoparticle potential energy.

Recognizing the waveform of a foreshock

The 2011 Mw9.1 Tohoku, Japan, earthquake is the paradigmatic example of an earthquake anticipated by a significant foreshock activity, with a Mw7.3 earthquake occurred two days before, within about 10 km 1. Recent results 2 show that statistically relevant changes can be found in the magnitude distribution after the Mw7.3 foreshock but the discrimination between normal and foreshock activity still remains a scientific challenge 3. Here we show that the envelope of the ground velocity recorded after the Mw7.3 foreshock presents an atypical sawtooth profile very different from the one observed after other earthquakes 4. We interpret this profile as the consequence of the locked state of the mainshock fault which reduces the possibility of the foreshock to trigger its own aftershocks. We find a similar sawtooth profile after other Mw6+ foreshocks followed within 10 days by a larger earthquake, as in the case of the 2014 Mw8.1 Iquique, Chile, sequence. This observation allows us to define a level of concern, simply extracted from the first 45 minutes of the recording waveform, associated to the occurrence of a larger earthquake. A test of the method for 47 Mw6+ worldwide earthquakes gives precise warning in time and space after all the 10 earthquakes followed by a larger one with only 2 false alerts.

On the advantages of operation in second-order diffraction of blazed gratings in soft X-ray monochromators

The fact that a diffraction grating can provide twofold-smaller bandwidth when operated in second-order diffraction is long known and applied routinely in the laboratory for spectroscopy in the visible and ultraviolet spectral range. A similar routine operation in monochromators for the soft X-ray range is not reported yet. This study will thus address the feasibility of efficient diffraction of soft X-rays in the second order at reflection gratings when operated at grazing angles of incidence. The related systematic study could make profitable use of a recently introduced simple analytical equation for the prediction of the diffraction efficiency of blazed gratings with an ideal sawtooth profile. The predictions are then verified by use of rigorous calculations. The principle finding is that, by operation of gratings with lower groove densities, and thus with higher efficiencies, in higher order diffraction, one can extend the tuning in existing instruments with mechanical/optical limitations to larger photon energies. The performance in terms of transmission and spectral resolving power can be very similar to the performance of a grating with a larger groove density, which would otherwise have to be used for accessing the same energy range. This would allow operation of a single highly efficient grating over a larger photon energy interval at a modern synchrotron radiation source, e.g. from 0.3 to 2.2 keV. Without any requirement for a sophisticated grating exchange scheme, a related instrument promises to be sufficiently stable for the needs imposed by the improvements in source point stability at diffraction-limited storage rings.

On Microfaceting Instability of Pt(110) Under Catalytic Oxidation of Adsorbed Co

ABSTRACTAs demonstrated by recent STM [1] and LEED [2] experiments the platinum (110) surface undergoes, at carbon monoxide submonolayer coverages, a phase transition from the 1 x 2 “missing-row” (reconstructed) state to the 1 x 1(bulk-like) state under specific temperature and partial-pressure conditions. The catalytic oxidation reaction CO + 1/2 → CO2 drives a microfaceting instability [3] [4] of the Pt(110) surface which ends up in a regular sawtooth profile with a period ≈ 200 Å, along the [110] direction.We introduce the idea that the rather extensive Pt mass transport, as involved in the process, could be energetically assisted by the reaction itself. Energy and momentum-balance considerations lead us to expect an energy ≲ 0.5 eV to be transferrable to thesubstrate. This should efficiently contribute to initiating the “scraping”process that leads to the microfaceted pattern.A simple model for nucleation and growth of facets is presented (see ref. 5), yielding characteristic times of order minutes (at T = 500 K), in fair agreement with experiment.Independently of the structural/catalytic problem, adsorption of CO at submonolayer coverages on, e.g., Pt(110) might be of interest from a surfactantphysics point of view (see ref. 6 for a very recent study on layer-by-layer homoepitaxial metal growth).