Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

Jamming for a 2D granular material

This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, . In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable which we identify with as c. It is possible to fit Z and P, to power law expressions in - c above c, and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near c. The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below c, where the application of shear strain at constant leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, τ. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant first leads to an increase of both τ and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only and τ, but also P. P, τ, and Z are all hysteretic functions of shear strain for fixed . However, we find that both P and τ are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, τ = μP. © 2010 The Royal Society of Chemistry.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Identification of beta-adrenergic receptors in human lymphocytes by (-) (3H) alprenolol binding.

Human lymphocytes are known to posessess a catecholamine-responsive adenylate cyclase which has typical beta-adrenergic specificity. To identify directly and to quantitate these beta-adenergic receptors in human lymphocytes, (-) [3H] alprenolol, a potent beta-adrenergic antagonist, was used to label binding sites in homogenates of human mononuclear leukocytes. Binding of (-) [3H] alprenolol to these sites demonstrated the kinetics, affinity, and stereospecificity expected of binding to adenylate cyclase-coupled beta-adrenergic receptors. Binding was rapid (t1/2 less than 30 s) and rapidly reversible (t1/2 less than 3 min) at 37 degrees C. Binding was a saturable process with 75 +/- 12 fmol (-) [3H] alprenolol bound/mg protein (mean +/- SEM) at saturation, corresponding to about 2,000 sites/cell. Half-maximal saturation occurred at 10 nM (-) [3H] alprenolol, which provides an estimate of the dissociation constant of (-) [3H] alprenolol for the beta-adrenergic receptor. The beta-adrenergic antagonist, (-) propranolol, potently competed for the binding sites, causing half-maximal inhibition of binding at 9 nM. beta-Adrenergic agonists also competed for the binding sites. The order of potency was (-) isoproterenol greater than (-) epinephrine greater than (-)-norepinephrine which agreed with the order of potency of these agents in stimulating leukocyte adenylate cyclase. Dissociation constants computed from binding experiments were virtually identical to those obtained from adenylate cyclase activation studies. Marked stereospecificity was observed for both binding and activation of adenylate cyclase. (-)Stereoisomers of beta-adrenergic agonists and antagonists were 9- to 300-fold more potent than their corresponding (+) stereoisomers. Structurally related compounds devoid of beta-adrenergic activity such as dopamine, dihydroxymandelic acid, normetanephrine, pyrocatechol, and phentolamine did not effectively compete for the binding sites. (-) [3H] alprenolol binding to human mononuclear leukocyte preparations was almost entirely accounted for by binding to small lymphocytes, the predominant cell type in the preparations. No binding was detectable to human erythrocytes. These results demonstrate the feasibility of using direct binding methods to study beta-adrenergic receptors in a human tissue. They also provide an experimental approach to the study of states of altered sensitivity to catecholamines at the receptor level in man.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

Weak coupling of acoustic-like phonons and magnon dynamics in incommensurate spin ladder compound Sr14Cu24O41

Intriguing lattice dynamics has been predicted for aperiodic crystals that contain incommensurate substructures. Here we report inelastic neutron scattering measurements of phonon and magnon dispersions in Sr14Cu24O41, which contains incommensurate one-dimensional (1D) chain and two-dimensional (2D) ladder substructures. Two distinct acoustic phonon-like modes, corresponding to the sliding motion of one sublattice against the other, are observed for atomic motions polarized along the incommensurate axis. In the long wavelength limit, it is found that the sliding mode shows a remarkably small energy gap of 1.7-1.9 meV, indicating very weak interactions between the two incommensurate sublattices. The measurements also reveal a gapped and steep linear magnon dispersion of the ladder sublattice. The high group velocity of this magnon branch and weak coupling with acoustic phonons can explain the large magnon thermal conductivity in Sr14Cu24O41 crystals. In addition, the magnon specific heat is determined from the measured total specific heat and phonon density of states, and exhibits a Schottky anomaly due to gapped magnon modes of the spin chains. These findings offer new insights into the phonon and magnon dynamics and thermal transport properties of incommensurate magnetic crystals that contain low-dimensional substructures.