Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

An algebraic theory of strong power in negatively connected exchange networks

Various extensions of the model are proposed to deal with a wider variety of conditions than are normally examined in experiments on exchange networks. With little or no modification, the model can predict power when exchange relations are unequal in value, when positions vary in the number of exchanges in which they can participate, and when three or more participants are required for a transaction to occur.

A structural and algebraic theory of power in negatively connected exchange networks can be deduced from a few simple and plausible assumptions about how individuals make decisions. The model generates a set of equations. A typology of exchange networks follows from characteristics of the solution to these equations. There are four possibilities: the equations have a unique solution in which some positions have all the power; the equations have a unique solution in which all positions have equal power; the equations have an infinity of solutions, in which case power is undetermined by structural considerations; the equations have no solution, in which case power should be unstable.     

The response of a spherical tissue-equivalent proportional counter to different heavy ions having similar velocities

A tissue-equivalent proportional counter (TEPC) has been used as a dosimeter in mixed radiation fields. Since it does not measure LET directly, the response function must be characterized in order to estimate quality factor and thus equivalent dose for the incident radiation. The objectives of this study were to measure the response of a spherical TEPC for different high-energy heavy ions (HZE) having similar velocity and to determine how quality factors can be determined. Data were obtained at the HIMAC heavy ion accelerator for ⁴He and ¹²C at (β=0.59) and ¹²C, ¹⁶O, ²⁸Si and ⁵⁶Fe at (β=0.70). A particle spectrometer recorded the charge and position of each incident beam particle. Events with low energy deposition were observed for particles that passed through the wall of the TEPC but not through the sensitive volume. The frequency averaged lineal energy, , was always less than the LET of the incident particles. The dose averaged lineal energy, , was approximately equal to LET for particles with LET greater than 10 keV/μm, whereas was larger than LET for the lighter particles with lower LET. Part of this effect is due to detector resolution and energy straggling that increases the variance of the response function. Although the TEPC is not a LET spectrometer, it can provide real time measurements of dose and provide estimates of quality factors for HZE particles using averaged values of lineal energy.     

Selective, controllable, and reversible aggregation of polystyrene latex microspheres via DNA hybridization

The directed three-dimensional self-assembly of microstructures and nanostructures through the selective hybridization of DNA is the focus of great interest toward the fabrication of new materials. Single-stranded DNA is covalently attached to polystyrene latex microspheres. Single-stranded DNA can function as a sequence-selective Velcro by only bonding to another strand of DNA that has a complementary sequence. The attachment of the DNA increases the charge stabilization of the microspheres and allows controllable aggregation of microspheres by hybridization of complementary DNA sequences. In a mixture of microspheres derivatized with different sequences of DNA, microspheres with complementary DNA form aggregates, while microspheres with noncomplementary sequences remain suspended. The process is reversible by heating, with a characteristic "aggregate dissociation temperature" that is predictably dependent on salt concentration, and the evolution of aggregate dissociation with temperature is observed with optical microscopy.     

Synthesis and barrier properties of poly(ε-caprolactone)-layered silicate nanocomposites

A new polymer-ceramic nanocomposite has been synthesized consisting of well-dispersed, two-dimensional layers of an organically modified mica-type silicate (MTS) within a degradable poly(ε-caprolactone) matrix. A protonated amino acid derivative of MTS was used to promote delamination/dispersion of the host layers and initiate ring-opening polymerization of ε-caprolactone monomer, resulting in poly(ε-caprolactone) chains that are ionically bound to the silicate layers. The polymer chains can be released from the silicate surface by a reverse ion-exchange reaction and were shown to be spectroscopically similar to pure poly(ε-caprolactone). Thick films of the polymer nanocomposite exhibit a significant reduction in water vapor permeability that shows a linear dependence on silicate content. The permeability of nanocomposite containing as low as 4.8% silicate by volume was reduced by nearly an order of magnitude compared to pure poly(ε-caprolactone). © 1995 John Wiley & Sons, Inc.     

Micro-scale and millimeter-scale rotating disk couette flows, experiments and analysis

Experimental results are presented for rotating Couette flows with and without circumferential pressure gradients between a rotating disk and a stationary fluid chamber. The spinning disk and the top of the C-shaped fluid chamber are separated by a μ-scale gap that forms the fluid chamber passage with inner and outer radii of 1.19 and 2.38 mm, respectively. Ranges of experimental conditions are presented to demonstrate the fluid dynamics of the test arrangement, and for determination of fluid viscosity, and gas slip flow accommodation coefficients. As such, the test arrangement provides means to determine such fluid and flow properties using microliter sample sizes, with relatively low magnitudes of experimental uncertainty.     

Time domain simulation in photonics: A comparison of nonlinear dispersive polarisation models

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.