Modified conjugated gradient method for diagonalising large matrices

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trail vectors, play a similar role of the conjugated gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitably for first principle calculations.Comment: 6 Pages, 2EPS figures. (To appear in Phys. Rev. E

Analysis by x-ray microtomography of a granular packing undergoing compaction

Several acquisitions of X-ray microtomography have been performed on a beads packing while it compacts under vertical vibrations. An image analysis allows to study the evolution of the packing structure during its progressive densification. In particular, the volume distribution of the pores reveals a large tail, compatible to an exponential law, which slowly reduces as the system gets more compact. This is quite consistent, for large pores, with the free volume theory. These results are also in very good agreement with those obtained by a previous numerical model of granular compaction.Comment: 4 pages, 4 figures. Latex (revtex4). to be published in Phys. Rev.

Reactive dynamics of inertial particles in nonhyperbolic chaotic flows

Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular enhancement of the production caused by the universal, underlying fractal patterns. The key dynamical invariant quantities are the effective fractal dimension and effective escape rate, which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets. The theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case. We introduce a class of dissipative embedding maps for numerical verification.Comment: Revtex, 5 pages, 2 gif figure

Glassy dynamics in granular compaction: sand on random graphs

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards' hypothesis for the athermal tapping dynamics.Comment: 13 pages Revtex, minor changes, to appear in PR

On the study of jamming percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property

The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in $Z$ and $r_0$ are 9$^\circ$ and 22\%, respectively, and the relative percent error in the numerical GS solutions is less than 10\%. We also make public the computer codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is ove

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick--slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy loading process. The model design leads to a systematic deficit of small scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.Comment: 24 pages, 11 figures, 2 tables, accepted for publication in Solar Physic

A new photon recoil experiment: towards a determination of the fine structure constant

We report on progress towards a measurement of the fine structure constant to an accuracy of $5\times 10^{-10}$ or better by measuring the ratio of the Planck constant to the mass of the cesium atom. Compared to similar experiments, ours is improved in three significant ways: (i) simultaneous conjugate interferometers, (ii) multi-photon Bragg diffraction between same internal states, and (iii) an about 1000 fold reduction of laser phase noise to -138 dBc/Hz. Combining that with a new method to simultaneously stabilize the phases of four frequencies, we achieve 0.2 mrad effective phase noise at the location of the atoms. In addition, we use active stabilization to suppress systematic effects due to beam misalignment.Comment: 12 pages, 9 figure

Axially and radially expandable modular helical soft actuator for robotic implantables

Soft robotics has advanced the field of biomedical engineering by creating safer technologies for interfacing with the human body. One of the challenges in this field is the realization of modular soft basic constituents and accessible assembly methods to increase the versatility of soft robots. We present a soft pneumatic actuator composed of two elastomeric strands that provide interdependent axial and radial expansion due to the modularity of the components and their helical arrangement. The actuator reaches 35% of elongation with respect to its initial height and both chambers achieve forces of 1N at about 19kPa. We describe the design, fabrication, modeling and benchtop testing of the soft actuator towards realizing 3D functional structures with potential medical applications. An example of application for soft medical robots is tissue regenerative for the long-gap esophageal atresia condition

Pb0.4Bi1.6Sr2Ca1Cu2O8+xPb_{0.4}Bi_{1.6}Sr_{2}Ca_{1}Cu_{2}O_{8+x} and Oxygen Stoichiometry: Structure, Resistivity, Fermi Surface Topology and Normal State Properties

$Pb_{0.4}Bi_{1.6}Sr_2CaCu_2O_{8+x}$ ($Bi(Pb)-$2212) single crystal samples were studied using transmission electron microscopy (TEM), $ab-$plane ($\rho_{ab}$) and $c-$axis ($\rho_c$) resistivity, and high resolution angle-resolved ultraviolet photoemission spectroscopy (ARUPS). TEM reveals that the modulation in the $b-$axis for $Pb(0.4)-$doped $Bi(Pb)-$2212 is dominantly of $Pb-$type that is not sensitive to the oxygen content of the system, and the system clearly shows a structure of orthorhombic symmetry. Oxygen annealed samples exhibit a much lower $c-$axis resistivity and a resistivity minimum at $80-130$K. He-annealed samples exhibit a much higher $c-$axis resistivity and $d\rho_c/dT<0$ behavior below 300K. The Fermi surface (FS) of oxygen annealed $Bi(Pb)-$2212 mapped out by ARUPS has a pocket in the FS around the $\bar{M}$ point and exhibits orthorhombic symmetry. There are flat, parallel sections of the FS, about 60\% of the maximum possible along $k_x = k_y$, and about 30\% along $k_x = - k_y$. The wavevectors connecting the flat sections are about $0.72(\pi, \pi)$ along $k_x = k_y$, and about $0.80(\pi, \pi)$ along $k_x = - k_y$, rather than $(\pi,\pi)$. The symmetry of the near-Fermi-energy dispersing states in the normal state changes between oxygen-annealed and He-annealed samples.Comment: APS_REVTEX 3.0, 49 pages, including 11 figures, available upon request. Submitted to Phys. Rev. B