Modeling Two Dimensional Magnetic Domain Patterns

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an externally applied magnetic field is varied. The main objective of this contribution is to present the results of a model that yields a rich pattern structure that closely resembles what is observed experimentally. Our model is a generalized two-dimensional Ising-like spin-one Hamiltonian with long-range interactions, which also incorporates anisotropy and Zeeman terms. The model is studied numerically, by means of Monte Carlo simulations. Changing the model parameters stripes, labyrinth and/or cellular domain structures are generated. For a variety of cases we display the patterns, determine the average size of the domains, the ordering transition temperature, specific heat, magnetic susceptibility and hysteresis cycle. Finally, we examine the reversibility of the pattern evolution under variations of the applied magnetic field. The results we obtain are in good qualitative agreement with experiment.Comment: 8 pages, 12 figures, submitted to Phys. Rev.

Patterns in Illinois Educational School Data

We examine Illinois educational data from standardized exams and analyze primary factors affecting the achievement of public school students. We focus on the simplest possible models: representation of data through visualizations and regressions on single variables. Exam scores are shown to depend on school type, location, and poverty concentration. For most schools in Illinois, student test scores decline linearly with poverty concentration. However Chicago must be treated separately. Selective schools in Chicago, as well as some traditional and charter schools, deviate from this pattern based on poverty. For any poverty level, Chicago schools perform better than those in the rest of Illinois. Selective programs for gifted students show high performance at each grade level, most notably at the high school level, when compared to other Illinois school types. The case of Chicago charter schools is more complex. In the last six years, their students' scores overtook those of students in traditional Chicago high schools.Comment: 9 pages, 6 figure

Thin Film Formation During Splashing of Viscous Liquids

After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, $t_{ejt}$, depends on impact velocity, liquid viscosity, gas pressure and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.Comment: 8 pages, 11 figure

Reply to "Comment on `Jamming at zero temperature and zero applied stress: The epitome of disorder' "

We answer the questions raised by Donev, Torquato, Stillinger, and Connelly in their "Comment on "Jamming at zero temperature and zero applied stress: The epitome of disorder.' " We emphasize that we follow a fundamentally different approach than they have done to reinterpret random close packing in terms of the "maximally random jammed" framework. We define the "maximally random jammed packing fraction" to be where the largest number of initial states, chosen completely randomly, have relaxed final states at the jamming threshold in the thermodynamic limit. Thus, we focus on an ensemble of states at the jamming threshold, while DTSC are interested in determining the amount of order and degree of jamming for a particular configuration. We also argue that soft-particle systems are as "clean" as those using hard spheres for studying jammed packings and point out the benefits of using soft potentials

Intruders in the Dust: Air-Driven Granular Size Separation

Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, non-monotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and show how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.Comment: 5 pages, 4 figure

Finite-Size Scaling at the Jamming Transition

We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions, indicating an upper critical dimension of 2.Comment: 5 pages, 3 figure

Ideal isotropic auxetic networks from random networks

Auxetic materials are characterized by a negative Poisson's ratio, $\mathrm{\nu}$. As the Poisson's ratio becomes negative and approaches the lower isotropic mechanical limit of $\mathrm{\nu = -1}$, materials show enhanced resistance to impact and shear, making them suitable for applications ranging from robotics to impact mitigation. Past experimental efforts aimed at reaching the $\mathrm{\nu = -1}$ limit have resulted in highly anisotropic materials, which show a negative Poisson's ratio only when subjected to deformations along specific directions. Isotropic designs have only attained moderately auxetic behavior, or have led to structures that cannot be manufactured in 3D. Here, we present a design strategy to create isotropic structures from disordered networks that leads to Poisson's ratios as low as $\mathrm{\nu = -0.98}$. The materials conceived through this approach are successfully fabricated in the laboratory and behave as predicted. The Poisson's ratio $\mathrm{\nu}$ is found to depend on network structure and bond strengths; this sheds light on the structural motifs that lead to auxetic behavior. The ideas introduced here can be generalized to 3D, a wide range of materials, and a spectrum of length scales, thereby providing a general platform that could impact technology.Comment: 16 pages, 6 figure