1,563 research outputs found
Some Combinatorial Operators in Language Theory
Multitildes are regular operators that were introduced by Caron et al. in
order to increase the number of Glushkov automata. In this paper, we study the
family of the multitilde operators from an algebraic point of view using the
notion of operad. This leads to a combinatorial description of already known
results as well as new results on compositions, actions and enumerations.Comment: 21 page
Supersymmetric moduli of the SU(2) x R linear dilaton background and NS5-branes
We study several classes of marginal deformations of the conformal field
theory SU(2) x R. This theory describes the near-horizon region of a stack of
parallel and coincident NS5-branes and is related holographically to little
string theory. We investigate the supersymmetry properties of these
deformations and we elucidate their role in the context of holography. The
conformal field theory moduli space contains "non-holographic" operators that
do not seem to have a simple interpretation in little string theory.
Subsequently, we analyze several NS5-brane configurations in terms of SU(2) x R
deformations. We discuss in detail interesting phenomena, like the excision of
the strong coupling region associated with the linear dilaton and the
manifestation of the symmetries of an NS5-brane setup in the deforming
operators. Finally, we present a class of conformally hyperkaehler geometries
that arise as "non-holographic" deformations of SU(2) x R.Comment: 38 pages, 1 figure, 1 table; version to appear in JHE
Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions
The aim of this paper is to design the polynomial construction of a finite
recognizer for hairpin completions of regular languages. This is achieved by
considering completions as new expression operators and by applying derivation
techniques to the associated extended expressions called hairpin expressions.
More precisely, we extend partial derivation of regular expressions to
two-sided partial derivation of hairpin expressions and we show how to deduce a
recognizer for a hairpin expression from its two-sided derived term automaton,
providing an alternative proof of the fact that hairpin completions of regular
languages are linear context-free.Comment: 28 page
Partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers
Cadabra: reference guide and tutorial
Cadabra is a computer algebra system for the manipulation of tensorial mathematical expressions such as they occur in “field theory problems”. It is aimed at, but not necessarily restricted to, high-energy physicists. It is constructed as a simple tree-manipulating core, a large collection of standalone algorithmic modules which act on the expression tree, and a set of modules responsible for output of nodes in the tree. All of these parts are written in C++. The input and output formats closely follow TEX, which in many cases means that cadabra is much simpler to use than other similar programs. It intentionally does not contain its own programming language; instead, new functionality is added by writing new modules in C++
Can hydrodynamic contact line paradox be solved by evaporation--condensation?
We investigate a possibility to regularize the hydrodynamic contact line
singularity in the configuration of partial wetting (liquid wedge on a solid
substrate) via evaporation-condensation, when an inert gas is present in the
atmosphere above the liquid. The no-slip condition is imposed at the
solid-liquid interface and the system is assumed to be isothermal. The mass
exchange dynamics is controlled by vapor diffusion in the inert gas and
interfacial kinetic resistance. The coupling between the liquid meniscus
curvature and mass exchange is provided by the Kelvin effect. The atmosphere is
saturated and the substrate moves at a steady velocity with respect to the
liquid wedge. A multi-scale analysis is performed. The liquid dynamics
description in the phase-change-controlled microregion and visco-capillary
intermediate region is based on the lubrication equations. The vapor diffusion
is considered in the gas phase. It is shown that from the mathematical point of
view, the phase exchange relieves the contact line singularity. The liquid mass
is conserved: evaporation existing on a part of the meniscus and condensation
occurring over another part compensate exactly each other. However, numerical
estimations carried out for three common fluids (ethanol, water and glycerol)
at the ambient conditions show that the characteristic length scales are tiny
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