173,751 research outputs found
Topological model for machining of parts with complex shapes
Complex shapes are widely used to design products in several industries such
as aeronautics, automotive and domestic appliances. Several variations of their
curvatures and orientations generate difficulties during their manufacturing or
the machining of dies used in moulding, injection and forging. Analysis of
several parts highlights two levels of difficulties between three types of
shapes: prismatic parts with simple geometrical shapes, aeronautic structure
parts composed of several shallow pockets and forging dies composed of several
deep cavities which often contain protrusions. This paper mainly concerns High
Speed Machining (HSM) of these dies which represent the highest complexity
level because of the shapes' geometry and their topology. Five axes HSM is
generally required for such complex shaped parts but 3 axes machining can be
sufficient for dies. Evolutions in HSM CAM software and machine tools lead to
an important increase in time for machining preparation. Analysis stages of the
CAD model particularly induce this time increase which is required for a wise
choice of cutting tools and machining strategies. Assistance modules for
prismatic parts machining features identification in CAD models are widely
implemented in CAM software. In spite of the last CAM evolutions, these kinds
of CAM modules are undeveloped for aeronautical structure parts and forging
dies. Development of new CAM modules for the extraction of relevant machining
areas as well as the definition of the topological relations between these
areas must make it possible for the machining assistant to reduce the machining
preparation time. In this paper, a model developed for the description of
complex shape parts topology is presented. It is based on machining areas
extracted for the construction of geometrical features starting from CAD models
of the parts. As topology is described in order to assist machining assistant
during machining process generation, the difficulties associated with tasks he
carried out are analyzed at first. The topological model presented after is
based on the basic geometrical features extracted. Topological relations which
represent the framework of the model are defined between the basic geometrical
features which are gathered afterwards in macro-features. Approach used for the
identification of these macro-features is also presented in this paper.
Detailed application on the construction of the topological model of forging
dies is presented in the last part of the paper
Distance-generalized Core Decomposition
The -core of a graph is defined as the maximal subgraph in which every
vertex is connected to at least other vertices within that subgraph. In
this work we introduce a distance-based generalization of the notion of
-core, which we refer to as the -core, i.e., the maximal subgraph in
which every vertex has at least other vertices at distance within
that subgraph. We study the properties of the -core showing that it
preserves many of the nice features of the classic core decomposition (e.g.,
its connection with the notion of distance-generalized chromatic number) and it
preserves its usefulness to speed-up or approximate distance-generalized
notions of dense structures, such as -club.
Computing the distance-generalized core decomposition over large networks is
intrinsically complex. However, by exploiting clever upper and lower bounds we
can partition the computation in a set of totally independent subcomputations,
opening the door to top-down exploration and to multithreading, and thus
achieving an efficient algorithm
A simple method for finite range decomposition of quadratic forms and Gaussian fields
We present a simple method to decompose the Green forms corresponding to a
large class of interesting symmetric Dirichlet forms into integrals over
symmetric positive semi-definite and finite range (properly supported) forms
that are smoother than the original Green form. This result gives rise to
multiscale decompositions of the associated Gaussian free fields into sums of
independent smoother Gaussian fields with spatially localized correlations. Our
method makes use of the finite propagation speed of the wave equation and
Chebyshev polynomials. It improves several existing results and also gives
simpler proofs.Comment: minor correction for t<
Supercritical super-Brownian motion with a general branching mechanism and travelling waves
We consider the classical problem of existence, uniqueness and asymptotics of
monotone solutions to the travelling wave equation associated to the parabolic
semi-group equation of a super-Brownian motion with a general branching
mechanism. Whilst we are strongly guided by the probabilistic reasoning of
Kyprianou (2004) for branching Brownian motion, the current paper offers a
number of new insights. Our analysis incorporates the role of Seneta-Heyde
norming which, in the current setting, draws on classical work of Grey (1974).
We give a pathwise explanation of Evans' immortal particle picture (the spine
decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient.
Moreover, in the spirit of Neveu's stopping lines we make repeated use of
Dynkin's exit measures. Additional complications arise from the general nature
of the branching mechanism. As a consequence of the analysis we also offer an
exact X(log X)^2 moment dichotomy for the almost sure convergence of the
so-called derivative martingale at its critical parameter to a non-trivial
limit. This differs to the case of branching Brownian motion and branching
random walk where a moment `gap' appears in the necessary and sufficient
conditions.Comment: 34 page
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Approximating the set of reachable states of a dynamical system is an
algorithmic yet mathematically rigorous way to reason about its safety.
Although progress has been made in the development of efficient algorithms for
affine dynamical systems, available algorithms still lack scalability to ensure
their wide adoption in the industrial setting. While modern linear algebra
packages are efficient for matrices with tens of thousands of dimensions,
set-based image computations are limited to a few hundred. We propose to
decompose reach set computations such that set operations are performed in low
dimensions, while matrix operations like exponentiation are carried out in the
full dimension. Our method is applicable both in dense- and discrete-time
settings. For a set of standard benchmarks, it shows a speed-up of up to two
orders of magnitude compared to the respective state-of-the art tools, with
only modest losses in accuracy. For the dense-time case, we show an experiment
with more than 10.000 variables, roughly two orders of magnitude higher than
possible with previous approaches
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