Force balance in canonical ensembles of static granular packings

We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Sticky Matter: Jamming and rigid cluster statistics with attractive particle interactions

While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.Comment: 4 pages, 5 figure

Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.Comment: 4 pages, 5 figures (revised text and one new figure). To appear in Phys. Rev. Let

Jamming in finite systems: stability, anisotropy, fluctuations and scaling

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.Comment: 20 pages, 12 figure

Relaxations and rheology near jamming

We determine the form of the complex shear modulus $G^*$ in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of $G^*$ on frequency and distance to the jamming transition, which is confirmed by numerics.Comment: 4 pages, 3 figure

High-resolution imaging at the SOAR telescope

Bright single and binary stars were observed at the 4.1-m telescope with a fast electron-multiplication camera in the regime of partial turbulence correction by the visible-light adaptive optics system. We compare the angular resolution achieved by simple averaging of AO-corrected images (long-exposure), selection and re-centering (shift-and-add or "lucky" imaging) and speckle interferometry. The effect of partial AO correction, vibrations, and image post-processing on the attained resolution is shown. Potential usefulness of these techniques is evaluated for reaching the diffraction limit in ground-based optical imaging. Measurements of 75 binary stars obtained during these tests are given and objects of special interest are discussed. We report tentative resolution of the astrometric companion to Zeta Aqr B. A concept of advanced high-resolution camera is outlined.Comment: Accepted for publication in PASP. 14 pages, 9 figures, 2 tabl

Analysis of Chaos-Induced Pulse Trains in the Ionization of Hydrogen

We examine excitation (by a short laser pulse) of a hydrogen atom in parallel electric and magnetic fields, from an initial tightly bound state to a state above the classical ionization threshold. We predict that the atom ionizes by emitting a train of electron pulses. This prediction is based on the classical dynamics of electron escape. In particular, the pulse train is due to classical chaos, which occurs for nonvanishing magnetic field. We connect the structure of the pulse train to fractal structure in the escape dynamics, and discuss several issues of experimental interest, with a particular emphasis on understanding the resolution of individual pulses. A brief account of this work appeared previously as a Letter [Phys. Rev. Lett. 92, 073001 (2004)]

Chaos-Induced Pulse Trains in the Ionization of Hydrogen

We predict that a hydrogen atom in parallel electric and magnetic fields, excited by a short laser pulse to an energy above the classical saddle, ionizes via a train of electron pulses. These pulses are a consequence of classical chaos induced by the magnetic field. We connect the structure of this pulse train (e.g., pulse size and spacing) to fractal structure in the classical dynamics. This structure displays a weak self-similarity, which we call “epistrophic self-similarity.” We demonstrate how this self-similarity is reflected in the pulse train