Maxwell's equations as a special case of deformation of a solid lattice in Euler's coordinates

It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topological defects as dislocations and disclinations, in the case of constant and homogenous expansion. The analogy between these two physical systems is complete, as it is not restricted to one of the two Maxwell's equation couples in the vacuum, but generalized to the two equation couples as well as to the diverse phenomena of dielectric polarization and magnetization of matter, just as to the electrical charges and the electrical currents. The eulerian approach of the solid lattice developed here includes Maxwell's equations as a special case, since it stems from a tensor theory, which is reduced to a vector one by contraction on the tensor indices. Considering the tensor aspect of the eulerian solid lattice deformation theory, the analogy can be extended to other physical phenomena than electromagnetism, a point which is shortly discussed at the end of the paper.Comment: 20 pages, 4 figures, 2 table

Finite temperature QMC study of the one-dimensional polarized Fermi gas

Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance. The temperature at which the "Fulde-Ferrell-Larkin-Ovchinnikov" (FFLO) phase is destroyed by thermal fluctuations is determined as a function of the polarization. It is shown that the presence of a confining potential does not dramatically alter the FFLO regime, and that recent experiments on trapped atomic gases likely lie just within the stable temperature range.Comment: 10 pages, 13 figures We added a discussion of the behaviour of the FFLO peak as a function of the attractive interaction strengt

Attractive Hubbard Model on a Honeycomb Lattice

We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the system undergoes a quantum phase transition at 5.0 < U_c/t < 5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered

Extreme events driven glassy behaviour in granular media

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: (1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.Comment: 7 pages, to appear in Europhys. Let

Electronic structure and optical properties of lightweight metal hydrides

We study the electronic structures and dielectric functions of the simple hydrides LiH, NaH, MgH2 and AlH3, and the complex hydrides Li3AlH6, Na3AlH6, LiAlH4, NaAlH4 and Mg(AlH4)2, using first principles density functional theory and GW calculations. All these compounds are large gap insulators with GW single particle band gaps varying from 3.5 eV in AlH3 to 6.5 eV in the MAlH4 compounds. The valence bands are dominated by the hydrogen atoms, whereas the conduction bands have mixed contributions from the hydrogens and the metal cations. The electronic structure of the aluminium compounds is determined mainly by aluminium hydride complexes and their mutual interactions. Despite considerable differences between the band structures and the band gaps of the various compounds, their optical responses are qualitatively similar. In most of the spectra the optical absorption rises sharply above 6 eV and has a strong peak around 8 eV. The quantitative differences in the optical spectra are interpreted in terms of the structure and the electronic structure of the compounds.Comment: 13 pages, 10 figure

A link between short-range and long-range properties of random sphere packings

We present a high precision particle-by-particle 3D reconstruction of granular systems composed of monodispersed spheres (sphere packings); the experimental approach is based on magnetic resonance imaging techniques. Our measurements revealed a strong correlation between the volume defined by the distance to the first nearest neighbor and the long-range average density. The main contribution to the amplitude decay of the correlation function can be described as exponential rather than power law up to a range equal to 7 sphere diameters. No evidence of geometrical structural changes as a function of the density was observed and neither regular crystallites nor any other statistically significant structures could be ascribed to a specific local arrangement. We concluded that granular compaction is the result of a process through which the system changes the average size of local structures without changing their local geometrical characteristics. These conclusions are supported by two-body correlation functions and Voronoi polyhedra space decomposition. The results provide a different perspective on the mechanisms underlying compaction with respect to previous works, and allow to discriminate between the different existing theoretical approache

DFT Study of Planar Boron Sheets: A New Template for Hydrogen Storage

We study the hydrogen storage properties of planar boron sheets and compare them to those of graphene. The binding of molecular hydrogen to the boron sheet (0.05 eV) is stronger than that to graphene. We find that dispersion of alkali metal (AM = Li, Na, and K) atoms onto the boron sheet markedly increases hydrogen binding energies and storage capacities. The unique structure of the boron sheet presents a template for creating a stable lattice of strongly bonded metal atoms with a large nearest neighbor distance. In contrast, AM atoms dispersed on graphene tend to cluster to form a bulk metal. In particular the boron-Li system is found to be a good candidate for hydrogen storage purposes. In the fully loaded case this compound can contain up to 10.7 wt. % molecular hydrogen with an average binding energy of 0.15 eV/H2.Comment: 19 pages, 7 figures, and 3 table

Effect of internal friction on transformation twin dynamics in SrxBa1-xSnO3 perovskite

The dynamics of transformation twins in SrxBa1-xSnO3 (x=0.6,0.8) perovskite has been studied by dynamical mechanical analysis in three-point bend geometry. This material undergoes phase transitions from orthorhombic to tetragonal and cubic structures on heating. The mechanical loss signatures of the transformation twins include relaxation and frequency-independent peaks in the orthorhombic and tetragonal phases, with no observed energy dissipation in the cubic phase. The macroscopic shape, orientation and relative displacements of twin walls have been calculated from bending and anisotropy energies. The mechanical loss angle and distribution of relaxation time are discussed in term of bending modes of domain walls.Comment: 20 pages, 4 figure

Constitutive relations for compressible granular flow in the inertial regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the μ(I),Φ(I)-rheology, which postulates that the bulk friction coefficient μ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction ϕ are functions of the inertial number I only. Although the μ(I),Φ(I)-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the μ(I),Φ(I)-rheology that does not suffer from such defects is proposed. In the framework of compressible I-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established μ(I) and Φ(I) relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations

Vibration-induced "thermally activated" jamming transition in granular media

The quasi-static frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency $f_{p}$ in the range $10^{-4}$ Hz to 5 Hz, while weak vibrations at high-frequency $f_{s}$, in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration, $\Gamma$, is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of $\Gamma$ or $f_{p}$. In a plot of $\ln f_{p}$ against $1/\Gamma$, the position of the peak follows an Arrhenius-like behaviour over four orders of magnitude in $f_{p}$. The data can be described as a stochastic hopping process involving a probability factor $\exp(-\Gamma_{j}/\Gamma)$ with $\Gamma_{j}$ a $f_{s}$-dependent characteristic vibration intensity. A $f_{s}$-independent description is given by $\exp(-\tau_{j}/\tau)$, with $\tau_{j}$ an intrinsic characteristic time, and $\tau =\Gamma ^{n}/2\pi f_{s}$, n=0.5-0.6, an empirical control parameter with unit of time. $\tau$ is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behaviour of the vibrated granular system, which, at the time-scale $1/f_{p}$, is solid-like at low $\Gamma$, and the oscillator is jammed into the granular material, and is fluid-like at high $\Gamma$, where the oscillator can slide viscously.Comment: Final version to appear in PR