Sums of roots of unity in cyclotomic fields

Let ζ_n denote a primitive nth root of unity, n ≥ 4. For any integer k, 2 ≤ k ≤ n ? 2 it is shown that the diophantine equation 1 + ζ_n + ? + ζ_n^k?1 = ?α^q has no solutions with ?, α in $\text{Q}$(ζ_n), ? a root of unity, α an algebraic integer, and q an integer ≥ 2, except when n = 10, 12, or 30, where the solutions are completely determined.     

Phonostat: thermostatting phonons in molecular dynamics simulations

Thermostat algorithms in a molecular dynamics simulation maintain an average temperature of a system by regulating the atomic velocities rather than the internal degrees of freedom. Herein, we present a "phonostat" algorithm that can regulate the total energy in a given internal degree of freedom. In this algorithm, the modal energies are computed at each time step using a mode-tracking scheme and then the system is driven by an external driving force of desired frequency and amplitude. The rate and amount of energy exchange between the phonostat and the system is controlled by two distinct damping parameters. Two different schemes for controlling the external driving force amplitude are also presented. In order to test our algorithm, the method is applied initially to a simple anharmonic oscillator for which the role of various phonostat parameters can be carefully tested. We then apply the phonostat to a more realistic (10,0) carbon nanotube system and show how such an approach can be used to regulate energy of highly anharmonic modes.     

Exploring the Potential of Fulvalene Dimetals as Platforms for Molecular Solar Thermal Energy Storage: Computations,Syntheses, Structures,Kinetics, and Catalysis

A study of the scope and limitations of varying the ligand framework around the dinuclear core of FvRu₂ in its function as a molecular solar thermal energy storage framework is presented. It includes DFT calculations probing the effect of substituents, other metals, and CO exchange for other ligands on ΔH_storage. Experimentally, the system is shown to be robust in as much as it tolerates a number of variations, except for the identity of the metal and certain substitution patterns. Failures include 1,1′,3,3′‐tetra‐tert‐butyl ( 4 ), 1,2,2′,3′‐tetraphenyl ( 9 ), diiron ( 28 ), diosmium ( 24 ), mixed iron‐ruthenium ( 27 ), dimolybdenum ( 29 ), and ditungsten ( 30 ) derivatives. An extensive screen of potential catalysts for the thermal reversal identified AgNO₃–SiO₂ as a good candidate, although catalyst decomposition remains a challenge.     

Hopf-algebraic structure of combinatorial objects and differential operators

A Hopf-algebraic structure on a vector space which has as basis a family of trees is described, and we survey some applications of this structure to combinatorics and to differential operators. Some possible future directions for this work are indicated. Supported in part by NASA Grant NAG 2-513. Supported in part by NSF Grant DMS 870-1085.     

Plasma isotope separation methods

Six major types of isotope separation methods which involve plasma phenomena are discussed. These methods are: plasma centrifuge, AVLIS (atomic vapor laser isotope separation), ion wave, ICR (ion cyclotron resonance), calutron, and gas discharge. The plasma phenomena in these major categories are described. An attempt is made to include enough references so that a more detailed study or evaluation of a particular method could readily be pursued. A brief discussion of isotope separation using mass balance concepts is also included     

Capillary electrophoresis of DNA in entangled polymer solutions.

Electrophoretic separations of DNA restriction fragments were performed in solutions of hydroxyethylcellulose (HEC) using capillary electrophoresis. Rheological studies confirmed that the entanglement threshold (phi*) for the solution is ca. 0.003 g/ml, in good agreement with theoretical predictions. A mesh size an order of magnitude smaller than that found in agarose gels was calculated using polymer-entanglement theory and was confirmed by electrophoretic measurements. Electrophoretic migration was shown to follow the Ogston regime under most conditions. An approach for obtaining smaller mesh sizes is presented.     

Correlated ejection of electron-hole drops from a continuously generated electron-hole liquid in Ge

The photocurrent power spectra were measured in a Ge photodiode as a function of the incident optical intensity at 1.8 K and 4.3 K. The observed spectra showed a peak at low frequencies superimposed on a continuum which has a cut-off at high frequency. The interpretation of the results implies that the electron-hole drops coming from a same region of the photoexcited liquid are ejected periodically.     

Model of a microwave beam coupling to CO2 laser plasma

We have designed a transmission line model of the microwave coupling mechanism for a microwave pumped CO₂ laser. The model is a total loss ridge waveguide transmission line having nonuniform impedance. The laser plasma is modeled as a frequency-dependent lossy dielectric and acts as a distributed resistance in the length of the microwave cavity. The coupling structure of the microwaves is designed not to be resonant at the microwave source frequency of 2.45 GHz at 1 kW and propagating the total microwave field energy to be absorbed without internal reflection. An exact solution to this general transmission line propagation constant for a shunt resistance along length of the guide is found. The measurements and predictions of the parameters of the plasma conductivity as a function of the attenuation constant agree closely.