An Inverse Scattering Transform for the Lattice Potential KdV Equation

The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation. These include discrete soliton solutions, Backlund transformations and an associated linear problem, called a Lax pair, for which it provides the compatibility condition. In this paper, we solve the initial value problem for the LKdV equation through a discrete implementation of the inverse scattering transform method applied to the Lax pair. The initial value used for the LKdV equation is assumed to be real and decaying to zero as the absolute value of the discrete spatial variable approaches large values. An interesting feature of our approach is the solution of a discrete Gel'fand-Levitan equation. Moreover, we provide a complete characterization of reflectionless potentials and show that this leads to the Cauchy matrix form of N-soliton solutions

Conductance through the disclination dipole defect in metallic carbon nanotubes

The electronic transport properties of a metallic carbon nanotube with the five-seven disclination pair characterized by a lattice distortion vector are investigated. The influence of the disclination dipole includes induced curvature and mixing of two sublattices. Both these factors are taken into account via a self-consistent perturbation approach. The conductance and the Fano factor are calculated within the transfer-matrix technique. PACS: 73.63.Fg, 72.80.Rj, 72.10.F

Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec

Picosecond electrical spectroscopy using monolithic GaAs circuits

This article describes an experimental apparatus for free-space mm-wave transmission measurements (spectroscopy). GaAs nonlinear transmission lines and sampling circuits are used as picosecond pulse generators and detectors, with planar monolithic bowtie antennas with associated substrate lenses used as the radiating and receiving elements. The received pulse is 270 mV amplitude and 2.4 ps rise time. Through Fourier transformation of the received pulse, 30–250 GHz measurements are demonstrated with <=0.3 dB (rms) accuracy

Pocket Gophers

Thirty-four species of pocket gophers, represented by five genera, occupy the western hemisphere. In the United States there are 13 species and three genera. The major features differentiating these genera are the size of their forefeet, claws, and front surfaces of their chisel-like incisors. Thomomys have smooth-faced incisors and small forefeet with small claws. Northern pocket gophers (Thomomys talpoides) are typically from 6 1/2 to 10 inches (17 to 25 cm) long. Their fur is variable in color but is often yellowish brown with pale underparts. Botta’s (or valley) pocket gophers (Thomomys bottae) are extremely variable in size and color. Botta’s pocket gophers are 5 inches to about 13 1/2 inches (13 to 34 cm) long. Their color varies from almost white to black. Geomys have two grooves on each upper incisor and large forefeet and claws. Plains pocket gophers (Geomys bursarius) vary in length from almost 7 1/2 to 14 inches (18 to 36 cm). Their fur is typically brown but may vary to black. Desert pocket gophers (Geomys arenarius) are always brown and vary from nearly 8 3/4 to 11 inches (22 to 28 cm) long. Texas pocket gophers (Geomys personatus) are also brown and are from slightly larger than 8 3/4 to nearly 13 inches (22 to 34 cm) long. Southeastern pocket gophers (Geomys pinetis) are of various shades of brown, depending on soil color, and are from 9 to 13 1/4 inches (23 to 34 cm) long. Pappogeomys have a single groove on each upper incisor and, like Geomys, have large forefeet with large claws. Yellow-faced pocket gophers (Pappogeomys castanops) vary in length from slightly more than 5 1/2 to just less than 7 1/2 inches (14 to 19 cm). Their fur color varies from pale yellow to dark reddish brown. The underparts vary from whitish to bright yellowish buff. Some hairs on the back and top of the head are dark-tipped. Range: Pocket gophers are found only in the Western Hemisphere. They range from Panama in the south to Alberta in the north. With the exception of the southeastern pocket gopher, they occur throughout the western two-thirds of the United States. Exclusion: Generally not practical. Small mesh wire fence may provide protection for ornamental trees and shrubs or flower beds. Plastic netting protects seedlings. Cultural Methods: Damage resistant varieties of alfalfa. Crop rotation. Grain buffer strips. Control of tap-rooted forbs. Flood irrigation. Plant naturally resistant varieties of seedlings. Repellents: Synthetic predator odors are all of questionable benefit. Toxicants: Baits: Strychnine alkaloid. Zinc phosphide. Chlorophacinone. Diphacinone. Fumigants: Carbon monoxide from engine exhaust. Others are not considered very effective, but some are used: Aluminum phosphide. Gas cartridges. Trapping: Various specialized gopher kill traps. Common spring or pan trap (sizes No. 0 and No. 1). Shooting: Not practical. Other: Buried irrigation pipe or electrical cables can be protected with cylindrical pipe having an outside diameter of at least 2.9 inches (7.4 cm). Surrounding a buried cable with 6 to 8 inches (15 to 20 cm) of coarse gravel (1 inch [2.5 cm] in diameter) may provide some protection

Pocket Gophers

Thirty-four species of pocket gophers, represented by five genera, occupy the western hemisphere. In the United States there are 13 species and three genera. The major features differentiating these genera are the size of their forefeet, claws, and front surfaces of their chisel-like incisors. Thomomys have smooth-faced incisors and small forefeet with small claws. Northern pocket gophers (Thomomys talpoides) are typically from 6 1/2 to 10 inches (17 to 25 cm) long. Their fur is variable in color but is often yellowish brown with pale underparts. Botta’s (or valley) pocket gophers (Thomomys bottae) are extremely variable in size and color. Botta’s pocket gophers are 5 inches to about 13 1/2 inches (13 to 34 cm) long. Their color varies from almost white to black. Geomys have two grooves on each upper incisor and large forefeet and claws. Plains pocket gophers (Geomys bursarius) vary in length from almost 7 1/2 to 14 inches (18 to 36 cm). Their fur is typically brown but may vary to black. Desert pocket gophers (Geomys arenarius) are always brown and vary from nearly 8 3/4 to 11 inches (22 to 28 cm) long. Texas pocket gophers (Geomys personatus) are also brown and are from slightly larger than 8 3/4 to nearly 13 inches (22 to 34 cm) long. Southeastern pocket gophers (Geomys pinetis) are of various shades of brown, depending on soil color, and are from 9 to 13 1/4 inches (23 to 34 cm) long. Pappogeomys have a single groove on each upper incisor and, like Geomys, have large forefeet with large claws. Yellow-faced pocket gophers (Pappogeomys castanops) vary in length from slightly more than 5 1/2 to just less than 7 1/2 inches (14 to 19 cm). Their fur color varies from pale yellow to dark reddish brown. The underparts vary from whitish to bright yellowish buff. Some hairs on the back and top of the head are dark-tipped. Range: Pocket gophers are found only in the Western Hemisphere. They range from Panama in the south to Alberta in the north. With the exception of the southeastern pocket gopher, they occur throughout the western two-thirds of the United States. Exclusion: Generally not practical. Small mesh wire fence may provide protection for ornamental trees and shrubs or flower beds. Plastic netting protects seedlings. Cultural Methods: Damage resistant varieties of alfalfa. Crop rotation. Grain buffer strips. Control of tap-rooted forbs. Flood irrigation. Plant naturally resistant varieties of seedlings. Repellents: Synthetic predator odors are all of questionable benefit. Toxicants: Baits: Strychnine alkaloid. Zinc phosphide. Chlorophacinone. Diphacinone. Fumigants: Carbon monoxide from engine exhaust. Others are not considered very effective, but some are used: Aluminum phosphide. Gas cartridges. Trapping: Various specialized gopher kill traps. Common spring or pan trap (sizes No. 0 and No. 1). Shooting: Not practical. Other: Buried irrigation pipe or electrical cables can be protected with cylindrical pipe having an outside diameter of at least 2.9 inches (7.4 cm). Surrounding a buried cable with 6 to 8 inches (15 to 20 cm) of coarse gravel (1 inch [2.5 cm] in diameter) may provide some protection

Monitoring the Low-Energy Gamma-Ray Sky Using Earth Occultation with GLAST GBM

Long term all-sky monitoring of the 20 keV – 2 MeV gamma-ray sky using the Earth occultation technique was demonstrated by the BATSE instrument on the Compton Gamma Ray Observatory. The principles and techniques used for the development of an end-to-end earth occultation data analysis system for BATSE can be extended to the GLAST Burst Monitor (GBM), resulting in multiband light curves and time-resolved spectra in the energy range 8 keV to above 1 MeV for known gamma-ray sources and transient outbursts, as well as the discovery of new sources of gamma-ray emission. In this paper we describe the application of the technique to the GBM. We also present the expected sensitivity for the GBM

Earth Occultation Imaging of the Low Energy Gamma-Ray Sky with GBM

The Earth Occultation Technique (EOT) has been applied to Fermi's Gamma-ray Burst Monitor (GBM) to perform all-sky monitoring for a predetermined catalog of hard X-ray/soft gamma-ray sources. In order to search for sources not in the catalog, thus completing the catalog and reducing a source of systematic error in EOT, an imaging method has been developed -- Imaging with a Differential filter using the Earth Occultation Method (IDEOM). IDEOM is a tomographic imaging method that takes advantage of the orbital precession of the Fermi satellite. Using IDEOM, all-sky reconstructions have been generated for ~sim 4 years of GBM data in the 12-50 keV, 50-100 keV and 100-300 keV energy bands in search of sources otherwise unmodeled by the GBM occultation analysis. IDEOM analysis resulted in the detection of 57 sources in the 12-50 keV energy band, 23 sources in the 50-100 keV energy band, and 7 sources in the 100-300 keV energy band. Seventeen sources were not present in the original GBM-EOT catalog and have now been added. We also present the first joined averaged spectra for four persistent sources detected by GBM using EOT and by the Large Area Telescope (LAT) on Fermi: NGC 1275, 3C 273, Cen A, and the Crab

General flux to a trap in one and three dimensions

The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in which the effective trap radius is reduced by an amount proportional to the jump length. This reduction in the effective trap radius corresponds to the Milne extrapolation length.Comment: Accepted for publication, in pres