A Sufficient Condition for Power Flow Insolvability with Applications to Voltage Stability Margins

For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient condition is constructed in a framework of an associated feasible, convex optimization problem. The objective employed in this optimization problem yields a measure of distance (in a parameter set) to the power flow solution boundary. In practical terms, this distance is closely related to quantities that previous authors have proposed as voltage stability margins. A typical margin is expressed in terms of the parameters of system loading (injected powers); here we additionally introduce a new margin in terms of the parameters of regulated bus voltages.Comment: 12 pages, 7 figure

The Relationship Between Distributive Leadership, School Culture, and Teacher Self-Efficacy at the Middle School Level

Recent and established research continues to demonstrate the need for school leaders to adapt their leadership practices to reflect the increasing demands associated with their role. This is particularly true for principals of large middle schools. Through the implementation of a distributive leadership framework, a principal can share responsibilities with qualified staff while promoting an institution-wide culture of trust that empowers teachers. The purpose of this correlational, quantitative research study was to examine the extent to which relationships exist between distributed leadership, school culture, and the self-efficacy of teachers within public middle schools in central New Jersey. This study was informed by Spillane’s and Elmore’s theoretical frameworks concerning distributed leadership, Bolman and Deal’s framework concerning school culture, and Bandura’s framework for self-efficacy. This study’s sample was 162 certified middle school teachers from five middle schools in central New Jersey. Each participating teacher completed a 73 question survey that gathered data on distributed leadership practices within their school, their school culture, and their view of their own self-efficacy. This quantitative data was collected utilizing the following three survey instruments: the Distributive Leadership Inventory (DLI), the School Culture Survey (SCS), and the Teacher Self-Efficacy Scale (TSES). Basic demographic information was also collected from the respondents. This study identified significant relationships between distributed leadership, school culture, and teacher self-efficacy. These results indicate the need for school leadership to adopt a holistic framework for leading large complex organizations such as middle schools. Within the current educational environment, it is essential for principals to understand and recognize the need for both formal and informal leaders within a school. Research has shown that successful school leaders create structures that encourage these formal and informal leaders to work collaboratively and build upon each other’s contributions to best practice in leadership and instruction. The implications of these findings, limitations of the study, and a suggested direction for future research on the relationships between distributive leadership, school culture, and teacher self-efficacy are also discussed

Collective Modes in a Dilute Bose-Fermi Mixture

We here study the collective excitations of a dilute spin-polarized Bose-Fermi mixture at zero temperature, considering in particular the features arising from the interaction between the two species. We show that a propagating zero-sound mode is possible for the fermions even when they do not interact among themselves.Comment: latex, 6 eps figure

Boson induced s-wave pairing in dilute boson-fermion mixtures

We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give an analytical method to derive the associated $T_c$ in the limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a $T_c$ of the same order as for a pure Fermi gas with bare attraction.Comment: 12 pages, no figure

Limits to Sympathetic Evaporative Cooling of a Two-Component Fermi Gas

We find a limit cycle in a quasi-equilibrium model of evaporative cooling of a two-component fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively the \beta\mu ~ 1. We speculate that one may be able to cool an atomic fermi gas further by photoassociating dimers near the bottom of the fermi sea.Comment: Submitted to Phys. Rev

Rapidly Rotating Fermi Gases

We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil

Ideal Quantum Gases in D-dimensional Space and Power-law Potentials

We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. Form such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose-Einstein condensation can set up in a confining power-law potential if and only if ${D/2}+{D/n}>1$, where $D$ is the space dimension and $n$ is the power-law exponent.Comment: 18 pages, Latex, to be published in Journal of Mathematical Physic

Resonant control of elastic collisions in an optically trapped Fermi gas of atoms

We have loaded an ultracold gas of fermionic atoms into a far off resonance optical dipole trap and precisely controlled the spin composition of the trapped gas. We have measured a magnetic-field Feshbach resonance between atoms in the two lowest energy spin-states, |9/2, -9/2> and |9/2, -7/2>. The resonance peaks at a magnetic field of 201.5 plus or minus 1.4 G and has a width of 8.0 plus or minus 1.1 G. Using this resonance we have changed the elastic collision cross section in the gas by nearly 3 orders of magnitude.Comment: 4 pages, 3 figure