5,534 research outputs found
D-Branes, Tachyons, and String Field Theory
In these notes we provide a pedagogical introduction to the subject of
tachyon condensation in Witten's cubic bosonic open string field theory. We use
both the low-energy Yang-Mills description and the language of string field
theory to explain the problem of tachyon condensation on unstable D-branes. We
give a self-contained introduction to open string field theory using both
conformal field theory and overlap integrals. Our main subjects are the Sen
conjectures on tachyon condensation in open string field theory and the
evidence that supports these conjectures. We conclude with a discussion of
vacuum string field theory and projectors of the star-algebra of open string
fields. We comment on the possible role of string field theory in the
construction of a nonperturbative formulation of string theory that captures
all possible string backgrounds.Comment: 103 pages, 11 figures. Lectures presented at TASI 2001. v2:
references added. v3: minor errors corrected; reference, discussion added
regarding other results on open string spectrum in stable vacuu
Frequency-Domain Analysis of Linear Time-Periodic Systems
In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature
Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories
The construction of multigrid operators for disordered linear lattice
operators, in particular the fermion matrix in lattice gauge theories, by means
of algebraic multigrid and block LU decomposition is discussed. In this
formalism, the effective coarse-grid operator is obtained as the Schur
complement of the original matrix. An optimal approximation to it is found by a
numerical optimization procedure akin to Monte Carlo renormalization, resulting
in a generalized (gauge-path dependent) stencil that is easily evaluated for a
given disorder field. Applications to preconditioning and relaxation methods
are investigated.Comment: 43 pages, 14 figures, revtex4 styl
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
We compare the effectiveness of solving Dirichlet-Neumann problems via the
Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit
formulation, the dual AFM formulation (AFM*), a boundary integral collocation
method (BIM), and the transformed field expansion (TFE) method. The first three
methods involve highly ill-conditioned intermediate calculations that we show
can be overcome using multiple-precision arithmetic. The latter two methods
avoid catastrophic cancellation of digits in intermediate results, and are much
better suited to numerical computation.
For the Craig-Sulem expansion, we explore the cancellation of terms at each
order (up to 150th) for three types of wave profiles, namely band-limited,
real-analytic, or smooth. For the AFM and AFM* methods, we present an example
in which representing the Dirichlet or Neumann data as a series using the AFM
basis functions is impossible, causing the methods to fail. The example
involves band-limited wave profiles of arbitrarily small amplitude, with
analytic Dirichlet data. We then show how to regularize the AFM and AFM*
methods by over-sampling the basis functions and using the singular value
decomposition or QR-factorization to orthogonalize them. Two additional
examples are used to compare all five methods in the context of water waves,
namely a large-amplitude standing wave in deep water, and a pair of interacting
traveling waves in finite depth.Comment: 31 pages, 18 figures. (change from version 1: corrected error in
table on page 12
- …