Shock wave theory for rupture of rubber

This article presents a theory for the rupture of rubber. Unlike conventional cracks, ruptures in rubber travel faster than the speed of sound, and consist in two oblique shocks that meet at a point. Physical features of rubber needed for this phenomenon include Kelvin dissipation and an increase of toughness as rubber retracts. There are three levels of theoretical description: an approximate continuum theory, an exact analytical solution of a slightly simplified discrete problem, and numerical solution of realistic and fully nonlinear equations of motion.Comment: 4 pages and 2 figure

A Problem with STEM

Striking differences between physics and biology have important implications for interdisciplinary science, technology, engineering, and mathematics (STEM) education. I am a physicist with interdisciplinary connections. The research group in which I work, the Center for Nonlinear Dynamics at the University of Texas at Austin, is converting into the physics department home for biological physics. Many ofmycollaborations have been with faculty in engineering. For the past 15 years, I have been codirector of the program at the University of Texas at Austin that prepares secondary science and mathematics teachers (UTeach, 2012). The future teachers take a course on scientific research I developed and deliver together with colleagues from biology, astronomy, chemistry, and biochemistry (Marder, 2011). This background naturally makes me an enthusiastic advocate of interdisciplinary education at the secondary and undergraduate levels. Yet at the same time, I am worried by some features of what may be coming. These worries have to do with what can happen as we are all lumped together under the heading of STEM.National Science FoundationPhysic

Dynamics of Simple Cracks

Cracks are the major vehicle for material failure, and often exhibit rather complex dynamics. The laws that govern their motion have remained an object of constant study for nearly a century. The simplest kind of dynamic crack is a single crack that moves along a straight line. We first briefly review current understanding of this "simple" object. We then critically examine the assumptions of the classic, scale-free, theory of dynamic fracture, and note when it works and how it may fail if certain of these assumptions are relaxed. A number of examples is provided, where the introduction of physical scales into this scale-free theory profoundly affects both a crack's structure and the resulting dynamics.Comment: 36 pages, 8 figures, a review paper submitted to "Annual Review of Condensed Matter Physics

Field induced phase transitions in the helimagnet Ba2CuGe2O7

We present a theoretical study of the two-dimensional spiral antiferromagnet Ba2CuGe2O7 in the presence of an external magnetic field. We employ a suitable nonlinear sigma model to calculate the T=0 phase diagram and the associated low-energy spin dynamics for arbitrary canted fields, in general agreement with experiment. In particular, when the field is applied parallel to the c axis, a previously anticipated Dzyaloshinskii-type incommensurate-to-commensurate phase transition is actually mediated by an intermediate phase, in agreement with our earlier theoretical prediction confirmed by the recent observation of the so-called double-k structure. The sudden pi/2 rotations of the magnetic structures observed in experiment are accounted for by a weakly broken U(1) symmetry of our model. Finally, our analysis suggests a nonzero weak-ferromagnetic component in the underlying Dzyaloshinskii-Moriya anisotropy, which is important for quantitative agreement with experiment.Comment: 17 pages, 14 figures. Corrected typos in the abstrac

The shape of the edge of a leaf

Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is to discuss a collection of analytical and numerical results for the shape of a sheet with a non--flat metric. First, a simple condition is found to determine when a stretched sheet folded into a cylinder loses axial symmetry, and buckles like a flower. General expressions are next found for the energy of stretched sheet, both in forms suitable for numerical investigation, and for analytical studies in the continuum. The bulk of the paper focuses upon long thin strips of material with a linear gradient in metric. In some special cases, the energy--minimizing shapes of such strips can be determined analytically. Euler--Lagrange equations are found which determine the shapes in general. The paper closes with numerical investigations of these equations.Comment: 15 pages and 6 figure

Tearing of free-standing graphene

We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by experimental configurations that expose graphene sheets to out-of-plane forces, such as back-gate voltage. We establish the geometry and basic energetics of failure and obtain approximate analytical expressions for critical crack lengths and forces. We also propose a method to obtain graphene's toughness. We observe that the cracks' path and the edge structure produced are dependent on the initial crack length. This work may help avoid the tearing of graphene sheets and aid the production of samples with specific edge structures.CAPESNational Science Foundation DMR 1002428Physic

Effect of 1 wt% LiF additive on the densification of nanocrystalline Y2O3 ceramics by spark plasma sintering

Densification of nanocrystalline cubic yttria (nc-Y2O3) powder, with 18 nm crystal size and 1 wt% LiF as a sintering additive was investigated. Specimens were fabricated by spark plasma sintering at 100 MPa, within the temperature range of 700–1500 °C. Sintering at 700 °C for 5 and 20 min resulted in 95% and 99.7% dense specimens, with an average grain size of 84 and 130 nm, respectively. nc-Y2O3 without additive was only 65% dense at 700 °C for 5 min. The presence of LiF at low sintering temperatures facilitated rapid densification by particle sliding and jamming release. Sintering at high temperatures resulted in segregation of LiF to the grain boundaries and its entrapment as globular phase within the fast growing Y2O3 grains. The sintering enhancement advantage of LiF was lost at high SPS temperatures

Youth Employment

Youth employment is the norm in American society. Approximately 80% of youth report holding jobs during their high school years (National Research Council, 1998). Entry into the labor market often begins early, with about half of youth ages 12 and 13 reporting that they work (Rothstein & Herz, 2000). Although statistics are gathered regularly about youth employment in the general population, comparatively little was known about employment patterns of youth with disabilities until the National Longitudinal Transition Study (NLTS) collected data from 1987 to 1990 (see footnote 1). The National Longitudinal Transition Study-2 (NLTS2) (see footnote 2) began updating and expanding data on youth with disabilities in 2001, including information on employment. Information reported here comes from telephone interviews and a mail survey conducted in 2001 with parents and guardians of youth with disabilities, and from comparisons made with 1987 NLTS employment data. Findings from NLTS2 are generalizable to youth with disabilities nationally who were 13 to 16 years old in December of 2000, and to each of 12 federal disability categories and to each age group (e.g., all 13-year-old students with disabilities, all 14-year-old students with disabilities, etc.). According to parents' reports, almost 60% of youth with disabilities are employed during a 1-year period -- some at work-study jobs, but the vast majority at non-school-related jobs

Densification and polymorphic transition of multiphase Y2O3 nanoparticles during spark plasma sintering

Multiphase (MP) monoclinic and cubic Y2O3 nanoparticles, 40 nm in diameter, were densified by spark plasma sintering for 5–15 min and100 MPa at 1000 °C, 1100 °C, and 1500 °C. Densification started with pressure increase at room temperature. Densification stagnated during heating compared to the high shrinkage rate in cubic single-phase reference nanopowder. The limited densification of the MP nanopowder originated from the vermicular structure (skeleton) formed during the heating. Interface controlled monoclinic to cubic polymorphic transformation above 980 °C led to the formation of large spherical cubic grains within the vermicular matrix. This resulted in the loss of the nanocrystalline character and low final density

The synthesis of a symmetrically substituted α-octa(isopentoxy)anthralocyanine

α-Octa(isopentoxy)anthralocyanine has been synthesized and is found to have an unprecedented low-energy Q-band absorption and a low first oxidation potential