Optimal Time Step Length for Lagrangian Interacting-Particle Simulations of Diffusive Mixing

Abstract Gait variability is a marker of cognitive decline. However, there is limited understanding of the cortical regions associated with gait variability. We examined associations between regional cortical thickness and gait variability in a population-based sample of older people without dementia. Participants (n=350, mean age 71.9±7.1) were randomly selected from the electoral roll. Variability in step time, step length, step width and double support time (DST) were calculated as the standard deviation of each measure, obtained from the GAITRite walkway. MRI scans were processed through FreeSurfer to obtain cortical thickness of 68 regions. Bayesian regression was used to determine regional associations of mean cortical thickness and thickness ratio (regional thickness/overall mean thickness) with gait variability. Smaller overall cortical thickness was only associated with greater step width and step time variability. Smaller mean thickness in widespread regions important for sensory, cognitive and motor functions were associated with greater step width and step time variability. In contrast, smaller thickness in a few frontal and temporal regions were associated with DST variability and the right cuneus was associated with step length variability. Smaller thickness ratio in frontal and temporal regions important for motor planning, execution and sensory function and, greater thickness ratio in the anterior cingulate was associated with greater variability in all measures. Examining individual cortical regions is important in understanding the relationship between gray matter and gait variability. Cortical thickness ratio highlights that smaller regional thickness relative to global thickness may be important for the consistency of gait.

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BIASED RANDOM WALKS, PARTIAL DIFFERENTIAL EQUATIONS AND UPDATE SCHEMES

The ANZIAM Journal ◽

10.1017/s1446181113000369 ◽

2013 ◽

Vol 55 (2) ◽

pp. 93-108 ◽

Cited By ~ 2

Author(s):

JACK D. HYWOOD ◽

KERRY A. LANDMAN

Keyword(s):

Statistical Physics ◽

Planck Equation ◽

Step Length ◽

Physical Object ◽

Cell Diameter ◽

Agent Based Models ◽

Time Step ◽

Partial Differential ◽

Agent Based ◽

Random Walkers

AbstractThere is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a collection of noninteracting biased random walkers on a one-dimensional lattice is considered. The usual master equation approach requires that two continuum limits, involving three parameters, namely step length, time step and the random walk bias, approach zero in a specific way. We are interested in the case where the two limits are not consistent. New results are obtained using a Fokker–Planck equation and the results are highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to an accurate macroscopic description of stochastic local movement rules in agent-based models when the lattice spacing represents a physical object such as cell diameter.

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Estimation of Optimal Time Step and Compare with of ODE Solver of MATLAB Package of RLC Circuit using Numerical Methods

Daffodil International University Journal of Science and Technology ◽

10.3329/diujst.v7i1.9650 ◽

1970 ◽

Vol 7 (1) ◽

pp. 67-73 ◽

Cited By ~ 1

Author(s):

Sheikh Md Rabiul Islam

Keyword(s):

Mesh Size ◽

Paper Analysis ◽

Optimal Time ◽

Time Step ◽

Minimum Error ◽

Optimal Output ◽

Runge Kutta Method ◽

Rlc Circuit ◽

Matlab Package ◽

Theoretical Results

In this paper analysis of a RLC circuit model that has been described optimal time step and minimize of error using numerical method. The goal is to reach the optimal time response due to the input for which optimal output response reaches a minimum error and also compared with ODE solver of MATLAB packages for the different cell (mesh) size of the RLC model. Table is constructed of the model to evaluate optimal time step and also CPU time into the simulation using MATLAB 7.6.0(R2008a).The values of register, capacitor and inductor as well as electromagnetic force are obtained through the mathematical relations of the model. The general analysis of the RLC circuit due to the optimal time step and minimum error is developed after several analysis and operations. The theoretical results show effectiveness of optimized of the model. Keywords: Optimal time step; MATLAB; Trapezoidal; Implicit Euler; Runge-Kutta method; RLC circuit. DOI: http://dx.doi.org/10.3329/diujst.v7i1.9650 Daffodil International University Journal of Science and Technology Vol.7(1) 2012 67-73

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Algorithms for Solving Darcian Flow in Structured Porous Media

Acta Polytechnica ◽

10.14311/1829 ◽

2013 ◽

Vol 53 (4) ◽

Author(s):

Michal Kuráž ◽

Petr Mayer

Keyword(s):

Proper Time ◽

Time Integration ◽

Mass Term ◽

Step Length ◽

Richards Equation ◽

Parabolic Problems ◽

Computational Domain ◽

Wetting Front ◽

Time Step ◽

The Matrix

This paper presents several algorithms that were implemented in DRUtES [1], a new open source project. DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual porosity approach (modeling the flow of liquids in a porous medium). Mass balance consistency is crucial in any hydrological balance and contaminant transportation evaluations. An incorrect approximation of the mass term greatly depreciates the results that are obtained. An algorithm for automatic time step selection is presented, as the proper time step length is crucial for achieving accuracy of the Euler time integration method. Various problems arise with poor conditioning of the Richards equation: the computational domain is clustered into subregions separated by a wetting front, and the nonlinear constitutive functions cover a high range of values, while a very simple diagonal preconditioning method greatly improves the matrix properties. The results are presented here, together with an analysis.

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Intelligent Time-Stepping for Practical Numerical Simulation

10.2118/204002-ms ◽

2021 ◽

Author(s):

Soham Sheth ◽

Francois McKee ◽

Kieran Neylon ◽

Ghazala Fazil

Keyword(s):

Heuristic Method ◽

Simulation Models ◽

Model Complexity ◽

Large Field ◽

Optimal Time ◽

Time Step ◽

Non Linear ◽

Set Up ◽

Reservoir Simulator ◽

Step Selection

Abstract We present a novel reservoir simulator time-step selection approach which uses machine-learning (ML) techniques to analyze the mathematical and physical state of the system and predict time-step sizes which are large while still being efficient to solve, thus making the simulation faster. An optimal time-step choice avoids wasted non-linear and linear equation set-up work when the time-step is too small and avoids highly non-linear systems that take many iterations to solve. Typical time-step selectors use a limited set of features to heuristically predict the size of the next time-step. While they have been effective for simple simulation models, as model complexity increases, there is an increasing need for robust data-driven time-step selection algorithms. We propose two workflows – static and dynamic – that use a diverse set of physical (e.g., well data) and mathematical (e.g., CFL) features to build a predictive ML model. This can be pre-trained or dynamically trained to generate an inference model. The trained model can also be reinforced as new data becomes available and efficiently used for transfer learning. We present the application of these workflows in a commercial reservoir simulator using distinct types of simulation model including black oil, compositional and thermal steam-assisted gravity drainage (SAGD). We have found that history-match and uncertainty/optimization studies benefit most from the static approach while the dynamic approach produces optimum step-sizes for prediction studies. We use a confidence monitor to manage the ML time-step selector at runtime. If the confidence level falls below a threshold, we switch to traditional heuristic method for that time-step. This avoids any degradation in the performance when the model features are outside the training space. Application to several complex cases, including a large field study, shows a significant speedup for single simulations and even better results for multiple simulations. We demonstrate that any simulation can take advantage of the stored state of the trained model and even augment it when new situations are encountered, so the system becomes more effective as it is exposed to more data.

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Smartphone Monitoring of Gait and Balance During Irregular Surface Walking and Obstacle Crossing

Frontiers in Sports and Active Living ◽

10.3389/fspor.2020.560577 ◽

2020 ◽

Vol 2 ◽

Author(s):

Janeesata Kuntapun ◽

Patima Silsupadol ◽

Teerawat Kamnardsiri ◽

Vipul Lugade

Keyword(s):

Older Adults ◽

Intraclass Correlation ◽

Step Length ◽

Living Environment ◽

The Body ◽

Irregular Surface ◽

Time Step ◽

Free Living ◽

Obstacle Crossing ◽

Gait Adaptation

As gait adaptation is vital for successful locomotion, the development of field-based tools to quantify gait in challenging real-world environments are crucial. The aims of this study were to assess the reliability and validity of a smartphone-based gait and balance assessment while walking on unobstructed and obstructed terrains using two phone placements. Furthermore, age-related differences in smartphone-derived gait strategies when navigating different walking conditions and environments were evaluated. By providing a method for evaluating gait in the simulated free-living environment, results of this study can elucidate the strategies young and older adults utilize to navigate obstructed and unobstructed walking paths. A total of 24 young and older adults ambulated indoors and outdoors under three conditions: level walking, irregular surface walking, and obstacle crossing. Android smartphones placed on the body and in a bag computed spatiotemporal gait (i.e., velocity, step time, step length, and cadence) and balance (i.e., center of mass (COM) displacement), with motion capture and video used to validate parameters in the laboratory and free-living environments, respectively. Reliability was evaluated using the intraclass correlation coefficient and validity was evaluated using Pearson's correlation and Bland-Altman analysis. A three-way ANOVA was used to assess outcome measures across group, condition, and environment. Results showed that smartphones were reliable and valid for measuring gait across all conditions, phone placements, and environments (ICC2,1: 0.606–0.965; Pearson's r: 0.72–1.00). Although body and bag placement demonstrated similar results for spatiotemporal parameters, accurate vertical COM displacement could only be obtained from the body placement. Older adults demonstrated a longer step time and lower cadence only during obstacle crossing, when compared to young adults. Furthermore, environmental differences in walking strategy were observed only during irregular surface walking. In particular, participants utilized a faster gait speed and a longer step length in the free-living environment, compared to the laboratory environment. In conclusion, smartphones demonstrate the potential for remote patient monitoring and home health care. Along with being easy-to-use, inexpensive, and portable, smartphones can accurately evaluate gait during both unobstructed and obstructed walking, indoors and outdoors.

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Changes of gait characteristics in a child with femoral nerve injury: a 16-month follow-up case study

Biomedical Engineering / Biomedizinische Technik ◽

10.1515/bmt-2015-0153 ◽

2016 ◽

Vol 61 (3) ◽

pp. 359-367 ◽

Cited By ~ 1

Author(s):

Seonhong Hwang ◽

Jeong-Mee Park ◽

Youngho Kim

Keyword(s):

Stride Length ◽

Stance Phase ◽

Reaction Force ◽

Femoral Nerve ◽

Knee Extensor ◽

Rectus Femoris ◽

Step Length ◽

Time Step ◽

Major Function ◽

Penetrating Wound

Abstract An 11-year-old child was able to walk independently even though he had injured his femoral nerve severely due to a penetrating wound in the medial thigh. In this study, gait analysis was conducted five times totally for 16 months to observe the characteristics of the gait parameters, which enabled him to walk independently. The cadence, walking speed, stride length, step length, stride time, step time, double limb support, and single limb support all improved after the third test (GA3). Insufficient knee flexion during the stance phase, that was the main problem of the subject, improved from 0.96° to the normal level of 17.01°. Although hip extension was also insufficient at the first test it subsequently improved and reached the normal range at the GA5. The peaks of the ground reaction force curve were low at the initial tests. However, these eventually improved and reached the reference values. The knee extensor moment during the stance phase increased markedly at the last test. Although the child lost his femoral nerve function, he was able to walk independently by compensating for the major function of the rectus femoris. In order to facilitate shock-absorption and move the feet forward, he reduced both gait speed and stride length, respectively. The results of this study are expected to provide insight into how clinicians set up their therapy goals, while considering compensations and changes over time.

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