Functional Methods and Effective Potentials for Nonlinear Composites

A formulation of variational principles in terms of functional integrals is proposed for any type of local plastic potentials. The minimization problem is reduced to the computation of a path integral. This integral can be used as a starting point for different approximations. As a first application, it is shown how to compute to second-order the weak-disorder perturbative expansion of the effective potentials in random composite. The three-dimensional results of Suquet and Ponte-Casta\~neda (1993) for the plastic dissipation potential with uniform applied tractions are retrieved and extended to any space dimension, taking correlations into account. In addition, the viscoplastic potential is also computed for uniform strain rates.Comment: 20 pages, accepted for publication in JMP

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.Comment: 5 pages, 4 figure

Collective Atomic Recoil Laser as a synchronization transition

We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially-periodic force field can be interpreted as the rotation of a phase oscillator. This suggests a relationship with synchronization transitions occurring in globally coupled rotators. In fact, we show that whenever the field dynamics can be adiabatically eliminated, the model reduces to a self-consistent equation for the probability distribution of the atomic "phases". In this limit, there exists a formal equivalence with the Kuramoto model, though with important differences in the self-consistency conditions. Depending on the field-cavity detuning, we show that the onset of synchronized behavior may occur through either a first- or second-order phase transition. Furthermore, we find a secondary threshold, above which a periodic self-pulsing regime sets in, that is immediately followed by the unlocking of the forward-field frequency. At yet higher, but still experimentally meaningful, input intensities, irregular, chaotic oscillations may eventually appear. Finally, we derive a simpler model, involving only five scalar variables, which is able to reproduce the entire phenomenology exhibited by the original model

Diffraction of a Bose-Einstein Condensate in the Time Domain

We have observed the diffraction of a Bose-Einstein condensate of rubidium atoms on a vibrating mirror potential. The matter wave packet bounces back at normal incidence on a blue-detuned evanescent light field after a 3.6 mm free fall. The mirror vibrates at a frequency of 500 kHz with an amplitude of 3.0 nm. The atomic carrier and sidebands are directly imaged during their ballistic expansion. The locations and the relative weights of the diffracted atomic wave packets are in very good agreement with the theoretical prediction of Carsten Henkel et al. [1].Comment: submitted to Phys. Rev.

High resolution observations of friction-induced oxide and its interaction with the worn surface

A detailed transmission electron microscopy study of oxide and oxygen-containing phase formation during the sliding wear of metals, composites and coatings is provided. A wide range of different materials types are reported in order to compare and contrast their oxidational wear behaviour: a low carbon stainless steel, a H21 tool steel containing 7%TiC particles, a 17%Cr white iron,an Al–Si/30%SiC composite, an Al–alloy (6092)–15%Ni3Al composite and finally a 3rd generation TiAlN/CrN ‘superhard’ multilayer coating. For the ferrous alloys, nanoscale oxides and oxygen-containing phases were formed that exhibited excellent adhesion to the substrate. In all cases, an increase in oxide coverage of the surface was associated with a decrease in Lancaster wear coefficient. The oxide at the surface of the 316L and H21+7%TiC was found to deform with the substrate, forming a mechanically mixed layer that enhanced surface wear resistance. Evidence of oxidational wear is presented for the wear of the Al–Si–30%SiC composite, but this did not give a beneficial effect in wear, a result of the brittle nature of the oxide that resulted in detachment of fine (150nm) thick fragments. The worn surface of the Al–alloy (6092)–15%Ni3Al and TiAlN/CrN coating was characterized by reaction with the counterface and subsequent oxidation, the product of which enhanced wear resistance. The observations are related to the classical theory of oxidational wear

Implications of the spatial variability of infiltration-water chemistry for the investigation of a karst aquifer: a field study at Milandre test site, Swiss Jura

The Milandre test site is an ideal karstic aquifer for studying the spatial heterogeneity of groundwater chemistry. Numerous observation points can be sampled: the spring, the underground river and its tributaries, and boreholes at different depths. The main causes of the spatial variability of the chemical parameters are: nature and localisation of the input, the structure of the infiltration zone, chemical reactions (transit time vs. reaction kinetics) and mixing of different waters. Physico-chemical data on springs discharging from the karstic system represent the sum of this spatial heterogeneity. Therefore, it is difficult to interpret the global-chemical response with a simple mixing model of the aquifer subsystems (runoff, matrix reservoir, epikarst). Chemical constituents related to agricultural inputs show important seasonal variations (coefficient of variation approximately 15%) and parameters linked to rainfall (δ18O) and to the aquifer (Ca2+, HCO3 −) present variations of less than 5%. This result indicates the importance of water storage in the epikarstic aquifer for periods of a few month

Reaching micro-arcsecond astrometry with long baseline optical interferometry; application to the GRAVITY instrument

A basic principle of long baseline interferometry is that an optical path difference (OPD) directly translates into an astrometric measurement. In the simplest case, the OPD is equal to the scalar product between the vector linking the two telescopes and the normalized vector pointing toward the star. However, a too simple interpretation of this scalar product leads to seemingly conflicting results, called here "the baseline paradox". For micro-arcsecond accuracy astrometry, we have to model in full the metrology measurement. It involves a complex system subject to many optical effects: from pure baseline errors to static, quasi-static and high order optical aberrations. The goal of this paper is to present the strategy used by the "General Relativity Analysis via VLT InTerferometrY" instrument (GRAVITY) to minimize the biases introduced by these defects. It is possible to give an analytical formula on how the baselines and tip-tilt errors affect the astrometric measurement. This formula depends on the limit-points of three type of baselines: the wide-angle baseline, the narrow-angle baseline, and the imaging baseline. We also, numerically, include non-common path higher-order aberrations, whose amplitude were measured during technical time at the Very Large Telescope Interferometer. We end by simulating the influence of high-order common-path aberrations due to atmospheric residuals calculated from a Monte-Carlo simulation tool for Adaptive optics systems. The result of this work is an error budget of the biases caused by the multiple optical imperfections, including optical dispersion. We show that the beam stabilization through both focal and pupil tracking is crucial to the GRAVITY system. Assuming the instrument pupil is stabilized at a 4 cm level on M1, and a field tracking below 0.2$\lambda/D$, we show that GRAVITY will be able to reach its objective of 10$\mu$as accuracy.Comment: 14 pages. Accepted by A&