scholarly journals Uniform in time estimates for the weak error of the Euler method for SDEs and a pathwise approach to derivative estimates for diffusion semigroups

2021 ◽  
pp. 1
Author(s):  
D. Crisan ◽  
P. Dobson ◽  
M. Ottobre
Keyword(s):  
Euler Method ◽  
Time Estimates ◽  
Pathwise Approach ◽  
Weak Error

scholarly journals An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems

2021 ◽  
Author(s):  
Fabian Merle ◽  
Andreas Prohl
Keyword(s):  
A Priori ◽  
Approximation Error ◽  
Adaptive Method ◽  
Euler Method ◽  
Weak Approximation ◽  
A Posteriori ◽  
Time Stepping ◽  
Backward Equation ◽  
Adaptive Time ◽  
Weak Error

AbstractWe develop an adaptive algorithm for large SDE systems, which automatically selects (quasi-)deterministic time steps for the semi-implicit Euler method, based on an a posteriori weak error estimate. Main tools to construct the a posteriori estimator are the representation of the weak approximation error via Kolmogorov’s backward equation, a priori bounds for its solution and the Clark–Ocone formula. For a certain class of SDE systems, we validate optimal weak convergence order 1 of the a posteriori estimator, and termination of the adaptive method based on it within $${{\mathcal {O}}}(\mathtt{Tol}^{-1})$$ O ( Tol - 1 ) steps.

Tire Rolling Kinematics Model for an Intelligent Tire Based on an Accelerometer

2020 ◽  
Vol 48 (4) ◽  
pp. 287-314
Author(s):  
Yan Wang ◽  
Zhe Liu ◽  
Michael Kaliske ◽  
Yintao Wei
Keyword(s):  
Elastic Deformation ◽  
Estimation Algorithm ◽  
Force Sensor ◽  
Euler Method ◽  
Rolling Contact ◽  
Body Motion ◽  
Identification Algorithm ◽  
Active Perception ◽  
Kinematics Model ◽  
Ring Model

ABSTRACT The idea of intelligent tires is to develop a tire into an active perception component or a force sensor with an embedded microsensor, such as an accelerometer. A tire rolling kinematics model is necessary to link the acceleration measured with the tire body elastic deformation, based on which the tire forces can be identified. Although intelligent tires have attracted wide interest in recent years, a theoretical model for the rolling kinematics of acceleration fields is still lacking. Therefore, this paper focuses on an explicit formulation for the tire rolling kinematics of acceleration, thereby providing a foundation for the force identification algorithms for an accelerometer-based intelligent tire. The Lagrange–Euler method is used to describe the acceleration field and contact deformation of rolling contact structures. Then, the three-axis acceleration vectors can be expressed by coupling rigid body motion and elastic deformation. To obtain an analytical expression of the full tire deformation, a three-dimensional tire ring model is solved with the tire–road deformation as boundary conditions. After parameterizing the ring model for a radial tire, the developed method is applied and validated by comparing the calculated three-axis accelerations with those measured by the accelerometer. Based on the features of acceleration, especially the distinct peak values corresponding to the tire leading and trailing edges, an intelligent tire identification algorithm is established to predict the tire–road contact length and tire vertical load. A simulation and experiments are conducted to verify the accuracy of the estimation algorithm, the results of which demonstrate good agreement. The proposed model provides a solid theoretical foundation for an acceleration-based intelligent tire.

RELIABILITY OF TIME ESTIMATES

1957 ◽  
Vol 7 ◽  
pp. 23 ◽  
Author(s):  
PAUL BAKAN
Keyword(s):  
Time Estimates

Molecular phylogeny and divergence time estimates of Penaeid Shrimp Lineages (Decapoda: Penaeidae)

Zootaxa ◽  
2009 ◽  
Vol 2107 (1) ◽  
pp. 41-52 ◽  
Author(s):  
CAROLINA M VOLOCH ◽  
PABLO R FREIRE ◽  
CLAUDIA A M RUSSO
Keyword(s):  
Fossil Record ◽  
Divergence Time ◽  
Penaeid Shrimp ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Global Clock ◽  
Late Tertiary ◽  
The Family ◽  
Molecular Studies ◽  
Triassic Period

Fossil record of penaeids indicates that the family exists since the Triassic period, but extant genera appeared only recently in Tertiary strata. Molecular based divergence time estimates on the matter of penaeid radiation were never properly addressed, due to shortcomings of the global molecular clock assumptions. Here, we studied the diversification patterns of the family, uncovering, more specifically, a correlation between fossil and extant Penaeid fauna. For this, we have used a Bayesian framework that does not assume a global clock. Our results suggest that Penaeid genera originated between 20 million years ago and 43 million years ago, much earlier than expected by previous molecular studies. Altogether, these results promptly discard late Tertiary or even Quaternary hypotheses that presumed a major glaciations influence on the diversification patterns of the family.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals Estimating epidemiologic dynamics from cross-sectional viral load distributions

Science ◽  
2021 ◽  
pp. eabh0635
Author(s):  
James A. Hay ◽  
Lee Kennedy-Shaffer ◽  
Sanjat Kanjilal ◽  
Niall J. Lennon ◽  
Stacey B. Gabriel ◽  
...  
Keyword(s):  
Population Distribution ◽  
Quantitative Polymerase Chain Reaction ◽  
Cross Sectional ◽  
Outbreak Management ◽  
Viral Loads ◽  
Time Estimates ◽  
Load Distributions ◽  
Random Samples ◽  
Combining Data ◽  
Polymerase Chain

Estimating an epidemic’s trajectory is crucial for developing public health responses to infectious diseases, but case data used for such estimation are confounded by variable testing practices. We show that the population distribution of viral loads observed under random or symptom-based surveillance, in the form of cycle threshold (Ct) values obtained from reverse-transcription quantitative polymerase chain reaction testing, changes during an epidemic. Thus, Ct values from even limited numbers of random samples can provide improved estimates of an epidemic’s trajectory. Combining data from multiple such samples improves the precision and robustness of such estimation. We apply our methods to Ct values from surveillance conducted during the SARS-CoV-2 pandemic in a variety of settings and offer alternative approaches for real-time estimates of epidemic trajectories for outbreak management and response.

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