2,522 research outputs found
Quantitative exponential bounds for the renewal theorem with spread-out distributions
We establish explicit exponential convergence estimates for the renewal
theorem, in terms of a uniform component of the inter arrival distribution, of
its Laplace transform which is assumed finite on a positive interval, and of
the Laplace transform of some related random variable. Our proof is based on a
coupling construction relying on discrete-time Markovian structures that
underly the renewal processes and on Lyapunov-Doeblin type arguments.Comment: Accepted for publication in Markov Processes and Related Field
Bayesian analysis of 210Pb dating
In many studies of environmental change of the past few centuries, 210Pb
dating is used to obtain chronologies for sedimentary sequences. One of the
most commonly used approaches to estimate the ages of depths in a sequence is
to assume a constant rate of supply (CRS) or influx of `unsupported' 210Pb from
the atmosphere, together with a constant or varying amount of `supported'
210Pb. Current 210Pb dating models do not use a proper statistical framework
and thus provide poor estimates of errors. Here we develop a new model for
210Pb dating, where both ages and values of supported and unsupported 210Pb
form part of the parameters. We apply our model to a case study from Canada as
well as to some simulated examples. Our model can extend beyond the current CRS
approach, deal with asymmetric errors and mix 210Pb with other types of dating,
thus obtaining more robust, realistic and statistically better defined
estimates.Comment: 22 Pages, 4 Figure
Dynamic survival analysis: modelling the hazard function via ordinary differential equations
The hazard function represents one of the main quantities of interest in the
analysis of survival data. We propose a general approach for modelling the
dynamics of the hazard function using systems of autonomous ordinary
differential equations (ODEs). This modelling approach can be used to provide
qualitative and quantitative analyses of the evolution of the hazard function
over time. Our proposal capitalises on the extensive literature of ODEs which,
in particular, allow for establishing basic rules or laws on the dynamics of
the hazard function via the use of autonomous ODEs. We show how to implement
the proposed modelling framework in cases where there is an analytic solution
to the system of ODEs or where an ODE solver is required to obtain a numerical
solution. We focus on the use of a Bayesian modelling approach, but the
proposed methodology can also be coupled with maximum likelihood estimation. A
simulation study is presented to illustrate the performance of these models and
the interplay of sample size and censoring. Two case studies using real data
are presented to illustrate the use of the proposed approach and to highlight
the interpretability of the corresponding models. We conclude with a discussion
on potential extensions of our work and strategies to include covariates into
our framework.Comment: R and Python code available at: https://github.com/FJRubio67/ODESur
On narrowing coated conductor film: emergence of granularity-induced field hysteresis of transport critical current
Critical current density Jc in polycrystalline or granular superconducting
material is known to be hysteretic with applied field H due to the focusing of
field within the boundary between adjacent grains. This is of concern in the
so-called coated conductors wherein superconducting film is grown on a
granular, but textured surface of a metal substrate. While previous work has
mainly been on Jc determined using induced or magnetization currents, the
present work utilizes transport current via an applied potential in strip
geometry. It is observed that the effect is not as pronounced using transport
current, probably due to a large difference in criterion voltage between the
two types of measurements. However, when the films are narrowed by patterning
into 200-, 100-, or 80-micron, the hysteresis is clearly seen, because of the
forcing of percolation across higher-angle grain boundaries. This effect is
compared for films grown on ion-beam-assisted-deposited (IBAD) YSZ substrate
and those grown on rolling-assisted-biaxially-textures substrates (RABiTS)
which have grains that are about ten times larger. The hysteresis is more
pronounced for the latter, which is more likely to have a weak grain boundary
spanning the width of the microbridge. This is also of concern to applications
in which coated conductors will be striated in order to reduce of AC losses.Comment: text-only: 10 pages, plus 5 figures on 5 page
A Physics Based Surrogate Model in Bayesian Uncertainty Quantification involving Elliptic PDEs
The paper addresses Bayesian inferences in inverse problems with uncertainty
quantification involving a computationally expensive forward map associated
with solving a partial differential equations. To mitigate the computational
cost, the paper proposes a new surrogate model informed by the physics of the
problem, specifically when the forward map involves solving a linear elliptic
partial differential equation. The study establishes the consistency of the
posterior distribution for this surrogate model and demonstrates its
effectiveness through numerical examples with synthetic data. The results
indicate a substantial improvement in computational speed, reducing the
processing time from several months with the exact forward map to a few
minutes, while maintaining negligible loss of accuracy in the posterior
distribution
Charge injection instability in perfect insulators
We show that in a macroscopic perfect insulator, charge injection at a
field-enhancing defect is associated with an instability of the insulating
state or with bistability of the insulating and the charged state. The effect
of a nonlinear carrier mobility is emphasized. The formation of the charged
state is governed by two different processes with clearly separated time
scales. First, due to a fast growth of a charge-injection mode, a localized
charge cloud forms near the injecting defect (or contact). Charge injection
stops when the field enhancement is screened below criticality. Secondly, the
charge slowly redistributes in the bulk. The linear instability mechanism and
the final charged steady state are discussed for a simple model and for
cylindrical and spherical geometries. The theory explains an experimentally
observed increase of the critical electric field with decreasing size of the
injecting contact. Numerical results are presented for dc and ac biased
insulators.Comment: Revtex, 7pages, 4 ps figure
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