Nonlinear dynamics and surface diffusion of diatomic molecules

The motion of molecules on solid surfaces is of interest for technological applications, but it is also a theoretical challenge. We study the deterministic and thermal diffusive dynamics of a dimer moving on a periodic substrate. The deterministic motion of the dimer displays strongly nonlinear features and chaotic behavior. The dimer thermal diffusive dynamics deviates from simple Arrhenius behavior, due to the coupling between vibrational and translational degrees of freedom. In the low-temperature limit the dimer diffusion can become orders of magnitude larger than that of a single atom, as also found experimentally. The relation between chaotic deterministic dynamics and stochastic thermal diffusion is discussed.Comment: 4 pages, 4 figure

Power law load dependence of atomic friction

We present a theoretical study of the dynamics of a tip scanning a graphite surface as a function of the applied load. From the analysis of the lateral forces, we extract the friction force and the corrugation of the effective tip-surface interaction potential. We find both the friction force and potential amplitude to have a power law dependence on applied load with exponent $\sim 1.6$. We interpret these results as characteristic of sharp undeformable tips in contrast to the case of macroscopic and elastic microscopic contacts.Comment: 4 pages, 4 figure

Rheological properties vs Local Dynamics in model disordered materials at Low Temperature

We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale $t_{rel}$, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain the Herschel-Bulkley exponent on the basis of the size dependence of the heterogeneities on the shear rate.Comment: 9 pages, 7 figure

Supermodel Analysis of the Hard X-Ray Excess in the Coma Cluster

The Supermodel provides an accurate description of the thermal contribution by the hot intracluster plasma which is crucial for the analysis of the hard excess. In this paper the thermal emissivity in the Coma cluster is derived starting from the intracluster gas temperature and density profiles obtained by the Supermodel analysis of X-ray observables: the XMM-Newton temperature profile and the Rosat brightness distribution. The Supermodel analysis of the BeppoSAX/PDS hard X-ray spectrum confirms our previous results, namely an excess at the c.l. of ~4.8sigma and a nonthermal flux of 1.30+-0.40x 10^-11 erg cm^-2 s^-1 in the energy range 20-80 keV. A recent joint XMM-Newton/Suzaku analysis reports an upper limit of ~6x10^-12 erg cm^-2 s^-1 in the energy range 20-80 keV for the nonthermal flux with an average gas temperature of 8.45+-0.06 keV, and an excess of nonthermal radiation at a confidence level above 4sigma, without including systematic effects, for an average XMM-Newton temperature of 8.2 keV in the Suzaku/HXD-PIN FOV, in agreement with our earlier PDS analysis. Here we present a further evidence of the compatibility between the Suzaku and BeppoSAX spectra, obtained by our Supermodel analysis of the PDS data, when the smaller size of the HXD-PIN FOV and the two different average temperatures derived by XMM-Newton and by the joint XMM-Newton/Suzaku analysis are taken into account. The consistency of the PDS and HXD-PIN spectra reaffirms the presence of a nonthermal component in the hard X-ray spectrum of the Coma cluster. The Supermodel analysis of the PDS data reports an excess at c.l. above 4sigma also for the higher average temperature of 8.45 keV thanks to the PDS FOV considerably greater than the HXD-PIN FOV.Comment: 18 pages, 7 figures, accepted for publication in Ap

Random sequential adsorption and diffusion of dimers and k-mers on a square lattice

We have performed extensive simulations of random sequential adsorption and diffusion of $k$-mers, up to $k=5$ in two dimensions with particular attention to the case $k=2$. We focus on the behavior of the coverage and of vacancy dynamics as a function of time. We observe that for $k=2,3$ a complete coverage of the lattice is never reached, because of the existence of frozen configurations that prevent isolated vacancies in the lattice to join. From this result we argue that complete coverage is never attained for any value of $k$. The long time behavior of the coverage is not mean field and nonanalytic, with $t^{-1/2}$ as leading term. Long time coverage regimes are independent of the initial conditions while strongly depend on the diffusion probability and deposition rate and, in particular, different values of these parameters lead to different final values of the coverage. The geometrical complexity of these systems is also highlighted through an investigation of the vacancy population dynamics.Comment: 9 pages, 9 figures, to be published in the Journal of Chemical Physic

A strong form of the Quantitative Isoperimetric inequality

We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary

Mechanics of a continuum medium. Vol. III

This work presents the fundamental assumptions and the successive mathematical developments which allow to establish the complete field equations of a continuum. The aim is to be sufficiently general and self-content using, however, mathematical procedures which can be always understook by an engineer with a common background of Linear Algebra and elementary Differential Calculus

Chandra Observation of a 300 kpc Hydrodynamic Instability in the Intergalactic Medium of the Merging Cluster of Galaxies A3667

We present results from the combination of two Chandra pointings of the central region of the cluster of galaxies A3667. From the data analysis of the first pointing Vikhlinin et al. reported the discovery of a prominent cold front which is interpreted as the boundary of a cool gas cloud moving through the hotter ambient gas. Vikhlinin et al. discussed the role of the magnetic fields in maintaining the apparent dynamical stability of the cold front over a wide sector at the forward edge of the moving cloud and suppressing transport processes across the front. In this Letter, we identify two new features in the X-ray image of A3667: i) a 300 kpc arc-like filamentary X-ray excess extending from the cold gas cloud border into the hotter ambient gas; ii) a similar arc-like filamentary X-ray depression that develops inside the gas cloud. The temperature map suggests that the temperature of the filamentary excess is consistent with that inside the gas cloud while the temperature of the depression is consistent with that of the ambient gas. We suggest that the observed features represent the first evidence for the development of a large scale hydrodynamic instability in the cluster atmosphere resulting from a major merger. This result confirms previous claims for the presence of a moving cold gas cloud into the hotter ambient gas. Moreover it shows that, although the gas mixing is suppressed at the leading edge of the subcluster due to its magnetic structure, strong turbulent mixing occurs at larger angles to the direction of motion. We show that this mixing process may favor the deposition of a nonnegligible quantity of thermal energy right in the cluster center, affecting the development of the central cooling flow.Comment: Replaced to match version accepted for publication in ApJL; some changes on text. 4 pages, 3 color figures and 2 BW figures, emulateapj