725,958 research outputs found
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
The standard numerical approach to determining matrix elements of local
operators and width of resonances uses the finite volume dependence of energy
levels and matrix elements. Finite size corrections that decay exponentially in
the volume are usually neglected or taken into account using perturbation
expansion in effective field theory. Using two-dimensional sine-Gordon field
theory as "toy model" it is shown that some exponential finite size effects
could be much larger than previously thought, potentially spoiling the
determination of matrix elements in frameworks such as lattice QCD. The
particular class of finite size corrections considered here are mu-terms
arising from bound state poles in the scattering amplitudes. In sine-Gordon
model, these can be explicitly evaluated and shown to explain the observed
discrepancies to high precision. It is argued that the effects observed are not
special to the two-dimensional setting, but rather depend on general field
theoretic features that are common with models relevant for particle physics.
It is important to understand these finite size corrections as they present a
potentially dangerous source of systematic errors for the determination of
matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil
The Largest Subsemilattices of the Endomorphism Monoid of an Independence Algebra
An algebra \A is said to be an independence algebra if it is a matroid
algebra and every map \al:X\to A, defined on a basis of \A, can be
extended to an endomorphism of \A. These algebras are particularly well
behaved generalizations of vector spaces, and hence they naturally appear in
several branches of mathematics such as model theory, group theory, and
semigroup theory.
It is well known that matroid algebras have a well defined notion of
dimension. Let \A be any independence algebra of finite dimension , with
at least two elements. Denote by \End(\A) the monoid of endomorphisms of
\A. We prove that a largest subsemilattice of \End(\A) has either
elements (if the clone of \A does not contain any constant operations) or
elements (if the clone of \A contains constant operations). As
corollaries, we obtain formulas for the size of the largest subsemilattices of:
some variants of the monoid of linear operators of a finite-dimensional vector
space, the monoid of full transformations on a finite set , the monoid of
partial transformations on , the monoid of endomorphisms of a free -set
with a finite set of free generators, among others.
The paper ends with a relatively large number of problems that might attract
attention of experts in linear algebra, ring theory, extremal combinatorics,
group theory, semigroup theory, universal algebraic geometry, and universal
algebra.Comment: To appear in Linear Algebra and its Application
Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation
We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate
finite difference approximation to its dynamics. The analysis is based upon
centre manifold theory so we are assured that the finite difference model
accurately models the dynamics and may be constructed systematically. The
theory is applied after dividing the physical domain into small elements by
introducing insulating internal boundaries which are later removed. The
Kuramoto-Sivashinsky equation is used as an example to show how holistic finite
differences may be applied to fourth order, nonlinear, spatio-temporal
dynamical systems. This novel centre manifold approach is holistic in the sense
that it treats the dynamical equations as a whole, not just as the sum of
separate terms
Numerical approximations for a fully fractional Allen-Cahn equation
A finite element scheme for an entirely fractional Allen-Cahn equation with
non-smooth initial data is introduced and analyzed. In the proposed nonlocal
model, the Caputo fractional in-time derivative and the fractional Laplacian
replace the standard local operators. Piecewise linear finite elements and
convolution quadratures are the basic tools involved in the presented numerical
method. Error analysis and implementation issues are addressed together with
the needed results of regularity for the continuous model. Also, the asymptotic
behavior of solutions, for a vanishing fractional parameter and usual
derivative in time, is discussed within the framework of the Gamma-convergence
theory
User's guide to a system of finite-element supersonic panel flutter programs
The utilization and operation of a set of six computer programs for the prediction of panel flutter at supersonic speeds by finite element methods are described. The programs run individually to determine the flutter behavior of a flat panel where the finite elements which model the panel each have four degrees of freedom (DOF), a curved panel where the finite elements each have four DOF, and a curved panel where the finite elements each have six DOF. The panels are assumed to be of infinite aspect ratio and are subjected to either simply-supported or clamped boundary conditions. The aerodynamics used by these programs are based on piston theory. Application of the program is illustrated by sample cases where the number of beam finite elements equals four, the in-plane tension parameter is 0.0, the maximum camber to panel length ratio for a curved panel case is 0.05, and the Mach number is 2.0. This memorandum provides a user's guide for these programs, describes the parameters that are used, and contains sample output from each of the programs
- …