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

Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential

We argue that massless Dirac particles in two spatial dimensions with $1/r$ Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of arXiv:0707.4171. At small interaction and small randomness, there is an infra-red stable fixed curve which merges with the strongly interacting infra-red unstable line at a critical endpoint, along which the dynamical critical exponent $z=1$.Comment: 4 pages, 4 figure

A Knowledge-Based Approach to Configuration Layout, Justification, and Documentation

The design, development, and implementation of a prototype expert system which could aid designers and system engineers in the placement of racks aboard modules on the Space Station Freedom are described. This type of problem is relevant to any program with multiple constraints and requirements demanding solutions which minimize usage of limited resources. This process is generally performed by a single, highly experienced engineer who integrates all the diverse mission requirements and limitations, and develops an overall technical solution which meets program and system requirements with minimal cost, weight, volume, power, etc. This system architect performs an intellectual integration process in which the underlying design rationale is often not fully documented. This is a situation which lends itself to an expert system solution for enhanced consistency, thoroughness, documentation, and change assessment capabilities

Bostonia: The Boston University Alumni Magazine. Volume 29

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Dimensional renormalization: ladders to rainbows

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory for rainbow graphs and vertex (or scattering diagrams) at zero momentum transfer, in the context of dimensional renormalization, and we prove that the correct anomalous dimensions for those processes emerge in the limit D -> 4.Comment: RevTeX, no figure

Further information on the origin of the Yale and Oak Ridge wild-type strains of Neurospora crassa

Further information on the origin of the Yale and Oak Ridge wild-type strains of Neurospora crass

A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

An integrable discretization of KdV at large times

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.Comment: 12 page

Large-N theory of strongly commensurate dirty-bosons: absence of transition in two dimensions

The spherical limit of strongly commensurate dirty-bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions, and consequently that the ground state in the effective Anderson localisation problem always remains localised. As a result there is only a gapped Mott insulator phase in the theory. Comparisons with other studies and the parallel with disordered fermions in 2D are discussed. We conjecture that while for the physical cases N=2 (XY) and N=1 (Ising) the theory should have the ordered phase, it may not for N=3 (Heisenberg).Comment: 15 pages, 4 figures. Minor typographical errors correcte

Double-boost DC to DC converter

Abstract In this paper anew boost topology is proposed. The circuit is similar with two parallel boost dc-to-dc converters, but the two inductors are charged in parallel and release energy in series, thus enhancing the voltage boost ratio. After a short analysis of the circuit, a comparative study with other classic boost converter (single boost and two-cascade) is presented. The simulation results show a net improvement of the boost ratio for the new proposed topology