Nonlinear mobility of a driven system: Temperature and disorder effects

We consider the dissipative nonlinear dynamics of a model of interacting atoms driven over a substrate potential. The substrate parameters can be suitably tuned in order to introduce disorder effects starting from two geometrically opposed ideal cases: commensurate and incommensurate interfaces. The role of temperature is also investigated through the inclusion of a stochastic force via a Langevin molecular dynamics approach. Here, we focus on the most interesting tribological case of underdamped sliding dynamics. For different values of the chain stiffness, we evaluate the static friction threshold and consider the depinning transition mechanisms as a function of the applied driving force. As experimentally observed in QCM frictional measurements of adsorbed layers, we find that disorder operates differently depending on the starting geometrical configuration. For commensurate interfaces, randomness lowers considerably the chain depinning threshold. On the contrary, for incommensurate mating contacts, disorder favors static pinning destroying the possible frictionless (superlubric) sliding states. Interestingly, thermal and disorder effects strongly influence also the occurrence of parametric resonances inside the chain, capable of converting the kinetic energy of the center-of-mass motion into internal vibrational excitations. We comment on the nature of the different dynamical states and hysteresis (due to system bi-stability) observed at different increasing and decreasing strengths of the external force.     

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”) of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”) analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A₈₀B₂₀ , a ternary model system with components “A”, “B”, and “C” in ratios of A₈₈B₇C₅ (as in Al₈₈Y₇Fe₅ , and to atomic coordinates in a Zr₈₀Pt₂₀ system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.     

High-speed camera study of Stage III crack propagation in chemically strengthened glass

Thermally or chemically strengthened glass is more resistant to damage and breakage compared to non-strengthened glass. Both strengthening mechanisms are based on incorporation of a compressive stress profile in the surface of the glass, which must be balanced by an equivalent amount of integrated tensile stress in the interior of the glass. This tensile stress is believed to affect the kinetics of Stage III crack propagation upon fracture of the sample. In this study, we use a high-speed camera to perform direct measurement of the kinetics of Stage III fracture in a strengthened glass sample. Data including crack propagation speed, crack bifurcation distance, and bifurcation angles are collected at a rate of 500,000 frames per second and then characterized. The authors believe that these data will provide a foundation for understanding the physics of Stage III fracture in strengthened glass samples.     

Surface chemistry study of Mn-doped germanium nanowires

Single crystal germanium nanowires have been grown by vapour-liquid-solid deposition onto silicon oxide substrates with Au catalyst nanoparticles. They have been doped by two different techniques: Ge and Mn co-evaporation during growth and post-growth Mn implantation. Scanning electron microscopy images show that Mn-implanted nanowires have a lower surface density and a smaller average diameter (18.8 nm) than the un-doped ones and those Mn doped by co-deposition. The effectiveness of Mn doping has been verified by X-ray photoemission spectroscopy and by energy-dispersive X-ray measurements, indicating in the two cases significant Mn atomic concentration in the nanowire. X-ray diffraction indicates that the nanowires are single crystals and that they do not contain precipitates of Mn extrinsic phases. Both SEM and XPS experimental evidences are in line to indicate that the Mn doping by ion implantation is preferable with respect to that one performed by co-evaporation as it reduces the thickness of the outer oxide sheath of the nanowires and their diameter.     

The Dirac-Ramond operator on loops in flat space

In this paper, a rigorous construction of the S¹-equivariant Dirac operator (i.e., Dirac-Ramond operator) on the space of (mean zero) loops in is given and its equivariant L²-index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra.     

Polynomial Stability to Three-Dimensional Magnetoelastic Waves

In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.     

Ond-folds whose canonical bundle is not numerically effective,according to Mori and Kawamata

Sunto In questo lavoro si studiano le varietà non singolari di dimensione d il cui divisore canonico non è numericamente effettivo e si estendono alcuni dei risultati ottenuti da Mori nel caso d=3. CiÒ viene ottenuto mediante un uso sistematico della teoria di Mori dei raggi estremali e di un forte teorema di Kawamata-Shokurov. Quest'ultimo risultato fornisce una varietà normale Y e un morfismo : X Y che contrae un raggio estremale R e che dá la struttura di X. Se R è numericamente effettivo, dimY     

Strong oscillations in molecular valence photoemission intensities

Photoemission from the two outermost ionizations [highest occupied molecular orbitals (HOMO and HOMO-1)] of Mg(eta(5)-C(5)H(5))(2) has been studied with synchrotron radiation in the gas phase. Strong oscillations in the HOMO-1/HOMO ratio, qualitatively similar to those well-known for fullerenes, are found. Excellent agreement with the experimental ratio is provided by accurate cross section calculations both at the density-functional theory and time-dependent density-functional theory level, indicating that a many electron response has a minor role for this effect. A comparison with the calculated values for other metal sandwich compounds indicate that the presence of oscillations is a widespread phenomenon, and a potential source of interesting information on the structural and electronic properties of the target molecule.