4,475 research outputs found
The differentiation of hypoelliptic diffusion semigroups
Basic derivative formulas are presented for hypoelliptic heat semigroups and
harmonic functions extending earlier work in the elliptic case. Emphasis is
placed on developing integration by parts formulas at the level of local
martingales. Combined with the optional sampling theorem, this turns out to be
an efficient way of dealing with boundary conditions, as well as with finite
lifetime of the underlying diffusion. Our formulas require hypoellipticity of
the diffusion in the sense of Malliavin calculus (integrability of the inverse
Malliavin covariance) and are formulated in terms of the derivative flow, the
Malliavin covariance and its inverse. Finally some extensions to the nonlinear
setting of harmonic mappings are discussed
Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis
In this paper we use methods from Stochastic Analysis to establish Li-Yau
type estimates for positive solutions of the heat equation. In particular, we
want to emphasize that Stochastic Analysis provides natural tools to derive
local estimates in the sense that the gradient bound at given point depends
only on universal constants and the geometry of the Riemannian manifold locally
about this point
Efficient Generation of Geographically Accurate Transit Maps
We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator
of geographically accurate transit maps. The input to LOOM is data about the
lines of a given transit network, namely for each line, the sequence of
stations it serves and the geographical course the vehicles of this line take.
We parse this data from GTFS, the prevailing standard for public transit data.
LOOM proceeds in three stages: (1) construct a so-called line graph, where
edges correspond to segments of the network with the same set of lines
following the same course; (2) construct an ILP that yields a line ordering for
each edge which minimizes the total number of line crossings and line
separations; (3) based on the line graph and the ILP solution, draw the map. As
a naive ILP formulation is too demanding, we derive a new custom-tailored
formulation which requires significantly fewer constraints. Furthermore, we
present engineering techniques which use structural properties of the line
graph to further reduce the ILP size. For the subway network of New York, we
can reduce the number of constraints from 229,000 in the naive ILP formulation
to about 4,500 with our techniques, enabling solution times of less than a
second. Since our maps respect the geography of the transit network, they can
be used for tiles and overlays in typical map services. Previous research work
either did not take the geographical course of the lines into account, or was
concerned with schematic maps without optimizing line crossings or line
separations.Comment: 7 page
The study of creep in machine elements using finite element methods
Bibliography: pages 92-98.In this thesis a simplified analysis procedure is developed, in which creep laws are decoupled from damage laws, for the purposb of constructing methods of use in the early stages of high temperature design. The procedure is based on the creep and damage laws proposed by Kachanov and Rabotnov. The creep laws are normalised. with respect to a convenient normalising stress. As a consequence of this normalisation, the dependence of the creep law on the stress constant, the time and temperature functions, and the actual load level is removed. In addition, if the reference stress of the component is chosen as the normalising stress, the creep law becomes insensitive to the stress exponent. The non-dimensional creep laws are then implemented in a standard finite element scheme, from which the results of a stationary state creep analysis are then in non-dimensional form. In order to estimate rupture times, the maximum stationary stresses in a component are used together with the damage laws. Conservative failure criteria are derived from the creep and damage laws to extend the method to residual life assessment and damage monitoring. The procedure is illustrated and tested against simple examples and case studies
Stochastic structural analysis of engineering components using the finite element method
Bibliography: p. 113-123.This thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs without requiring major code development. These routines are implemented in the general purpose finite element program ABAQUS through its user element subroutine facility and two probabilistic finite elements are developed: a three-dimensional beam element limited to linear material behaviour and a two-dimensional plane element involving elastic-plastic material behaviour. The plane element incorporates plane strain, plane stress and axisymmetric formulations. The numerical accuracy and robustness of the routines are verified and application of the probabilistic finite element method is illustrated in two case studies, one involving a four-story, two-bay frame structure, the other a reactor pressure vessel nozzle. The probabilistic finite element routines developed in this thesis integrate point estimate methods and mean value first order methods within the same program. Both methods require a systematic sequence involving the perturbation of the random parameters to be evaluated, although the perturbation sequence of the methods differ. It is shown that computer-time saving techniques such as Taylor series and iterative perturbation schemes, developed for mean value based methods, can also be used to solve point estimate method problems. These efficient techniques are limited to linear problems; nonlinear problems must use full perturbation schemes. Finally, it is shown that all these probabilistic methods and perturbation schemes can be integrated within one program and can follow many of the existing deterministic program structures and subroutines. An overall strategy for converting deterministic finite element programs to probabilistic finite element programs is outlined
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