Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.Comment: Phys. Rev. E, (to be published, May 2005

A graph of dark energy significance on different spatial and mass scales

The current cosmological paradigm sees the formation and evolution of the cosmic large-scale structure as governed by the gravitational attraction of the Dark Matter (DM) and the repulsion of the Dark Energy (DE). We characterize the relative importance of uniform and constant dark energy, as given by the Lambda term in the standard LCDM cosmology, in galaxy systems of different scales, from groups to superclusters. An instructive "Lambda significance graph" is introduced where the matter-DE density ratio /rho_Lambda for different galaxy systems is plotted against the radius R. This presents gravitation and DE dominated regions and shows directly the zero velocity radius, the zero-gravity radius, and the Einstein-Straus radius for any fixed value of mass. Example galaxy groups and clusters from the local universe illustrate the use of the Lambda significance graph. These are generally located deep in the gravity-dominated region /rho_Lambda > 2, being virialized. Extended clusters and main bodies of superclusters can reach down near the border line between gravity-dominated and DE dominated regions /rho_Lambda = 2. The scale--mass relation from the standard 2-point correlation function intersects this balance line near the correlation lenght. The log /rho_Lambda vs. log R diagram is a useful and versatile way to characterize the dynamical state of systems of galaxies within the Lambda dominated expanding universe.Comment: 4 pages, 2 figure

Gas-Rich Companions of Isolated Galaxies

We have used the VLA to search for gaseous remnants of the galaxy formation process around six extremely isolated galaxies. We found two distinct HI clouds around each of two galaxies in our sample (UGC 9762 & UGC 11124). These clouds are rotating and appear to have optical counterparts, strongly implying that they are typical dwarf galaxies. The companions are currently weakly interacting with the primary galaxy, but have short dynamical friction timescales (~1 Gyr) suggesting that these triple galaxy systems will shortly collapse into one massive galaxy. Given that the companions are consistent with being in circular rotation about the primary galaxy, and that they have small relative masses, the resulting merger will be a minor one. The companions do, however, contain enough gas that the merger will represent a significant infusion of fuel to drive future star formation, bar formation, or central activity, while building up the mass of the disk thus making these systems important pieces of the galaxy formation and evolution process.Comment: Corrected dynamical friction calculation error. Revised discussion & conclusions. 7 pages, 4 tables, 6 figures, to appear in May 1999 Astronomical Journa

Coherent States For SU(3)

We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n,0) and (0,m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site.Comment: 18 pages, LaTeX, no figure

Production and implementation of a habitat suitability model for breeding Bald Eagles in the lower Chesapeake Bay (Phase II: Model construction through habitat mapping)

Since its elevation to endangered status in 1978, protection of the Bald Eagle and its habitat is governed by the Endangered Species Act. Under this designation, critical habitat is defined as any area essential to the survival and recovery of the species. Current habitat management strategies for nesting Bald Eagles are centered around the protection of active nest trees. Although this practice is essential, it does not address potential nesting habitat. Much habitat remains unoccupied that is both critical to the continued recovery and maintenance of the population and is under imminent risk of development. We quantified 61 topographic, land-use, and disturbance variables within 127 active eagle territories and around 127 randomly chosen points to evaluate their potential as predictors of habitat quality for breeding Bald Eagles. Fifty-four of 61 variables were significantly different between the two samples. Compared to random sites, eagles prefer to nest in areas situated close to large water bodies, away from extensive human disturbance, and having considerable forest cover. A discriminant function analysis was used to determine the linear combination of variables that best differentiate between active and random sites. Sixteen variables conformed to parametric assumptions and were entered into a step-wise discriminant function procedure. The final 4-variable model constructed produced a classification accuracy of 81.5%. In addition to the model variables, 4 distribution constraints were identified within the data set. A combination of these constraints and the 4-variable model were used in the final land classification model. The final model was used to classify lands along a 100 mi. reach of the James River and a 75 mi. reach of the Rappahannock River. All lands along these drainages or their tributaries that fell within 3 km of a channel at least 250 m wide were classified. This land mass included over 2,300 square kilometers. Classification of the area was accomplished by establishing a network of over 15,000 registration points, parameterizing the model variables for each point independently, and employing the classification model. A substantial portion of the James and Rappahannock River drainages (458 and 274 square kilometers respectively) was classified as unsuitable due to high housing density and/or the lack of adequate nesting substrate. However, a comparable portion of both drainages was also found to contain either good or very good habitat for breeding (344 and 349 square kilometers for the James and Rappahannock Rivers respectively). Relationships between habitat quality and the model variables were consistent with those expected based on the univariate results

Active land planning for long-term Bald Eagle management within the lower Chesapeake Bay (Phase I: Model construction)

Since its elevation to endangered status in 1978, protection of the Bald Eagle and its habitat is governed by the Endangered Species Act. Under this designation, critical habitat is defined as any area essential to the survival and recovery of the species. Current habitat management strategies for nesting Bald Eagles are centered around the protection of active nest trees. Although this practice is essential, it does not address potential nesting habitat. Much habitat remains unoccupied that is both critical to the continued recovery and maintenance of the population and is under imminent risk of development. We quantified 61 topographic, landuse, and disturbance variables within 127 active eagle territories and around 127 randomly chosen points to evaluate their potential as predictors of habitat quality for breeding Bald Eagles. Fifty-four of 61 variables were significantly different between the two samples. Compared to random sites, eagles prefer to nest in areas situated close to large water bodies, away from extensive human disturbance, and having considerable forest cover. A discriminant function analysis was used to determine the linear combination of variables that best differentiate between active and random sites. Sixteen variables conformed to parametric assumptions and were entered into a step-wise discriminant function procedure. The final 4-variable model constructed produced a classification accuracy of 81.5%. In addition to the model variables, 4 distribution constraints were identified within the data set. A combination of these constraints and the 4-variable model were used in the final land classification model

On the Green's Function of the almost-Mathieu Operator

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo

Polynomial-Time Simulation of Pairing Models on a Quantum Computer

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between ground and first excited states, and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultra-small metallic grains.Comment: 5 pages, RevTeX, Latest, modified version to appear in Phys. Rev. Let

Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge