Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Towards more accurate and reliable predictions for nuclear applications

The need for nuclear data far from the valley of stability, for applications such as nuclear as- trophysics or future nuclear facilities, challenges the robustness as well as the predictive power of present nuclear models. Most of the nuclear data evaluation and prediction are still performed on the basis of phenomenological nuclear models. For the last decades, important progress has been achieved in funda- mental nuclear physics, making it now feasible to use more reliable, but also more complex microscopic or semi-microscopic models in the evaluation and prediction of nuclear data for practical applications. In the present contribution, the reliability and accuracy of recent nuclear theories are discussed for most of the relevant quantities needed to estimate reaction cross sections and beta-decay rates, namely nuclear masses, nuclear level densities, gamma-ray strength, fission properties and beta-strength functions. It is shown that nowadays, mean-field models can be tuned at the same level of accuracy as the phenomenological mod- els, renormalized on experimental data if needed, and therefore can replace the phenomenogical inputs in the prediction of nuclear data. While fundamental nuclear physicists keep on improving state-of-the-art models, e.g. within the shell model or ab initio models, nuclear applications could make use of their most recent results as quantitative constraints or guides to improve the predictions in energy or mass domain that will remain inaccessible experimentally.

Nonlinear response of permanent dipoles in a uniaxial potential to alternating fields

It is shown how the existing theory of the dynamic Kerr effect and nonlinear dielectric relaxation based on the noninertial Brownian rotation of noninteracting rigid dipolar particles may be generalized to take into account interparticle interactions using the Maier-Saupe mean field potential. The results (available in simple closed form) suggest that the frequency dependent nonlinear response provides a method of measuring the Kramers escape rate (or in the analogous problem of magnetic relaxation of fine single domain ferromagnetic particles, the superparamagnetic relaxation time).

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

Generalized compound transport of charged particles in turbulent magnetized plasmas

The transport of charged particles in partially turbulent magnetic systems is investigated from first principles. A generalized compound transport model is proposed, providing an explicit relation between the mean-square deviation of the particle parallel and perpendicular to a magnetic mean field, and the mean-square deviation which characterizes the stochastic field-line topology. The model is applied in various cases of study, and the relation to previous models is discussed.

The Influence of Point Defects and Inhomogeneous Strain on the Functional Behaviour of Thin film Ferroelectrics

An attempt has been made to unequivocally identify the influence that inhomogeneous strain fields, surrounding point defects, have on the functional properties of thin film ferroelectrics. Single crystal thin film lamellae of BaTiO3 have been integrated into capacitor structures, and the functional differences between those annealed in oxygen and those annealed in nitrogen have been mapped. Key features, such as the change in the paraelectric-ferroelectric phase transition from first to second order were noted and found to be consistent with mean field modeling predictions for the effects of inhomogeneous strain. Switching characteristics appeared to be unaffected, suggesting that point defects have a low efficacy in domain wall pinning.

Nonconservative generalized current-induced forces

A recent result for the curl of forces on ions under steady-state current in atomic wires with noninteracting electrons is extended to generalized forces on classical degrees of freedom in the presence of mean-field electron-electron screening. Current is described within a generic multiterminal picture, forces within the Ehrenfest approximation, and screening within an adiabatic, but not necessarily spatially local, mean-field picture.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) >= 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

Random neighbor sandpile model with constrained total energy

We propose as energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n of each site, but the various exponents do not. For n = 6, we got that E-c = 0.4545; and a self-similar structure of the energy distribution function with five major peaks is also observed. This is a natural result of system dynamics and the way the system is disturbed.

Universality and self-similarity of an energy-constrained sandpile model with random neighbors

We study an energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n for each site, but the various exponents are independent of n. A self-similar structure with n-1 major peaks is developed for the energy distribution p(E) when the system approaches its stationary state. The avalanche dynamics contributes to the major peaks appearing at E-Pk = 2k/(2n - 1) with k = 1,2,...,n-1, while the fine self-similar structure is a natural result of the way the system is disturbed. [S1063-651X(99)10307-6].

Dynamical symmetry breaking with optimal control: Reducing the number of pieces

We analyze the production of defects during the dynamical crossing of a mean-field phase transition with a real order parameter. When the parameter that brings the system across the critical point changes in time according to a power-law schedule, we recover the predictions dictated by the well-known Kibble-Zurek theory. For a fixed duration of the evolution, we show that the average number of defects can be drastically reduced for a very large but finite system, by optimizing the time dependence of the driving using optimal control techniques. Furthermore, the optimized protocol is robust against small fluctuations.

Robust nonadiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of nonadiabatic electronic transitions and test it against exact integration of the time-dependent Schrodinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the nonadiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.

Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Positron scattering and annihilation on noble-gas atoms

Positron scattering and annihilation on noble-gas atoms is studied ab initio using many-body theory methods for positron energies below the positronium formation threshold. We show that in this energy range, the many-body theory yields accurate numerical results and provides a near-complete understanding of the positron–noble-gas atom system. It accounts for positron-atom and electron-positron correlations, including the polarization of the atom by the positron and the nonperturbative effect of virtual positronium formation. These correlations have a large influence on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter Zeff (effective number of electrons participating in annihilation) rise steeply along the sequence of noble-gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.