14,571 research outputs found
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a
natural way to any elastic material. The corresponding Lie algebroid, called
\textit{material algebroid}, is used to characterize the uniformity and the
homogeneity properties of the material. The relation to previous results in
terms of structures is discussed in detail. An illustrative example is
presented as an application of the theory
Functionally Graded Media
The notions of uniformity and homogeneity of elastic materials are reviewed
in terms of Lie groupoids and frame bundles. This framework is also extended to
consider the case Functionally Graded Media, which allows us to obtain some
homogeneity conditions.Comment: 20 pages, 5 figure
An analytically solvable model of probabilistic network dynamics
We present a simple model of network dynamics that can be solved analytically
for uniform networks. We obtain the dynamics of response of the system to
perturbations. The analytical solution is an excellent approximation for random
networks. A comparison with the scale-free network, though qualitatively
similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur
Quantum Noether Method
We present a general method for constructing consistent quantum field
theories with global symmetries. We start from a free non-interacting quantum
field theory with given global symmetries and we determine all consistent
perturbative quantum deformations assuming the construction is not obstructed
by anomalies. The method is established within the causal
Bogoliubov-Shirkov-Epstein-Glaser approach to perturbative quantum field theory
(which leads directly to a finite perturbative series and does not rely on an
intermediary regularization). Our construction can be regarded as a direct
implementation of Noether's method at the quantum level. We illustrate the
method by constructing the pure Yang-Mills theory (where the relevant global
symmetry is BRST symmetry), and the N=1 supersymmetric model of Wess and
Zumino. The whole construction is done before the so-called adiabatic limit is
taken. Thus, all considerations regarding symmetry, unitarity and anomalies are
well-defined even for massless theories.Comment: 53 pages, latex, version to appear in Nuclear Physics
A Robust AFPTAS for Online Bin Packing with Polynomial Migration
In this paper we develop general LP and ILP techniques to find an approximate
solution with improved objective value close to an existing solution. The task
of improving an approximate solution is closely related to a classical theorem
of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is
often applied in designing robust algorithms for online problems. We apply our
new techniques to the online bin packing problem, where it is allowed to
reassign a certain number of items, measured by the migration factor. The
migration factor is defined by the total size of reassigned items divided by
the size of the arriving item. We obtain a robust asymptotic fully polynomial
time approximation scheme (AFPTAS) for the online bin packing problem with
migration factor bounded by a polynomial in . This answers
an open question stated by Epstein and Levin in the affirmative. As a byproduct
we prove an approximate variant of the sensitivity theorem by Cook at el. for
linear programs
Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies
summary:We present a general geometrical theory of uniform bodies which includes three-dimensional Cosserat bodies, rods and shells as particular cases. Criteria of local homogeneity are given in terms on connections
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