Charter School Funding: Inequity in the City

Public charter schools are a growing part of K-12 education. Charter schools are public schools that are granted operational autonomy by their authorizing agency in return for a commitment to achieve specific performance goals. Like traditional public schools, charter schools are free to students and overseen by the state. Unlike traditional public schools, however, most charters are open to all students who wish to apply, regardless of where they live. If a charter school is over-subscribed, usually random lotteries determine which students will be admitted. Most charter schools are independent of the traditional public school district in which they operate

Entropy and Temperature of a Static Granular Assembly

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics, which is founded on the principle of conservation of energy, provides this framework. Grains, however, are small but macroscopic objects whose interactions are dissipative since energy can be lost through excitations of the internal degrees of freedom. In this work, we construct a statistical framework for static, mechanically stable packings of grains, which parallels that of equilibrium statistical mechanics but with conservation of energy replaced by the conservation of a function related to the mechanical stress tensor. Our analysis demonstrates the existence of a state function that has all the attributes of entropy. In particular, maximizing this state function leads to a well-defined granular temperature for these systems. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks. Our demonstration that a statistical ensemble can be constructed through the identification of conserved quantities other than energy is a new approach that is expected to open up avenues for statistical descriptions of other non-equilibrium systems.Comment: 5 pages, 4 figure

Damage areas on selected LDEF aluminum surfaces

With the U.S. about to embark on a new space age, the effects of the space environment on a spacecraft during its mission lifetime become more relevant. Included among these potential effects are degradation and erosion due to micrometeoroid and debris impacts, atomic oxygen and ultraviolet light exposure as well as material alteration from thermal cycling, and electron and proton exposure. This paper focuses on the effects caused by micrometeoroid and debris impacts on several LDEF aluminum plates from four different bay locations: C-12, C-10, C-01, and E-09. Each plate was coated with either a white, black, or gray thermal paint. Since the plates were located at different orientations on the satellite, their responses to the hypervelocity impacts varied. Crater morphologies range from a series of craters, spall zones, domes, spaces, and rings to simple craters with little or no spall zones. In addition, each of these crater morphologies is associated with varying damage areas, which appear to be related to their respective bay locations and thus exposure angles. More than 5% of the exposed surface area examined was damaged by impact cratering and its coincident effects (i.e., spallation, delamination and blow-off). Thus, results from this analysis may be significant for mission and spacecraft planners and designers

A tail-like assembly at the portal vertex in intact herpes simplex type-1 virions

Herpes viruses are prevalent and well characterized human pathogens. Despite extensive study, much remains to be learned about the structure of the genome packaging and release machinery in the capsids of these large and complex double-stranded DNA viruses. However, such machinery is well characterized in tailed bacteriophage, which share a common evolutionary origin with herpesvirus. In tailed bacteriophage, the genome exits from the virus particle through a portal and is transferred into the host cell by a complex apparatus (i.e. the tail) located at the portal vertex. Here we use electron cryo-tomography of human herpes simplex type-1 (HSV-1) virions to reveal a previously unsuspected feature at the portal vertex, which extends across the HSV-1 tegument layer to form a connection between the capsid and the viral membrane. The location of this assembly suggests that it plays a role in genome release into the nucleus and is also important for virion architecture

Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N < 16), we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady-state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.Comment: 18 pages, 23 figures, 5 table

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step, square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure

Measurements of the Yield Stress in Frictionless Granular Systems

We perform extensive molecular dynamics simulations of 2D frictionless granular materials to determine whether these systems can be characterized by a single static yield shear stress. We consider boundary-driven planar shear at constant volume and either constant shear force or constant shear velocity. Under steady flow conditions, these two ensembles give similar results for the average shear stress versus shear velocity. However, near jamming it is possible that the shear stress required to initiate shear flow can differ substantially from the shear stress required to maintain flow. We perform several measurements of the shear stress near the initiation and cessation of flow. At fixed shear velocity, we measure the average shear stress $\Sigma_{yv}$ in the limit of zero shear velocity. At fixed shear force, we measure the minimum shear stress $\Sigma_{yf}$ required to maintain steady flow at long times. We find that in finite-size systems $\Sigma_{yf} > \Sigma_{yv}$, which implies that there is a jump discontinuity in the shear velocity from zero to a finite value when these systems begin flowing at constant shear force. However, our simulations show that the difference $\Sigma_{yf} - \Sigma_{yv}$, and thus the discontinuity in the shear velocity, tend to zero in the infinite system size limit. Thus, our results indicate that in the large system limit, frictionless granular systems are characterized by a single static yield shear stress. We also monitor the short-time response of these systems to applied shear and show that the packing fraction of the system and shape of the velocity profile can strongly influence whether or not the shear stress at short times overshoots the long-time average value.Comment: 7 pages and 6 figure

The calcium current in inner segments of rods from the salamander (Ambystoma tigrinum) retina.

Solitary rod inner segments were isolated from salamander retinae. Their Ca current was studied with the 'whole-cell, gigaseal' technique (Hamill, Marty, Neher, Sakmann & Sigworth, 1981). The soluble constituents of the cytoplasm exchanged with the solution in the pipette. The external solution could be changed during continuous perfusion. Membrane voltage was controlled with a voltage clamp. After permeant ions other than Ca were replaced with impermeant ions (i.e. tetraethylammonium as a cation, and aspartate or methanesulphonate as an anion), an inward current remained. It activated at approximately -40 mV, reached a maximum at approximately 0 mV, and decreased as the membrane was further depolarized. The size of the current increased when Ba was substituted for external Ca. The current was blocked when Ca was replaced with Co. The voltage at which the current was half-maximum shifted from approximately -22 to -31 mV during the initial 3 min of an experiment. The maximum amplitude of the current continuously declined during the entire course of an experiment. The time course for activation of the Ca current following a step of depolarization could be described by the sum of two exponentials. The time constant of the slower exponential was voltage dependent. Deactivation following repolarization could also be described by the sum of two exponentials. Both time constants for deactivation were independent of voltage (between -30 and 0 mV) and faster than the slower time constant for activation. When the internal Ca concentration was buffered by 10 mM-EGTA, the Ca current did not inactivate during several seconds of maintained depolarization. When the concentration of EGTA was reduced to 0.1 mM, the Ca current declined and the membrane conductance decreased during several seconds of maintained depolarization. This inactivation was incomplete and only occurred after a substantial quantity of Ca entered. Following repolarization the Ca conductance recovered from inactivation. In contrast, the continuous decline observed during the course of an experiment (item 3) was not reversible. The difference suggests that inactivation and the decline are distinct processes