scholarly journals A separated representation involving multiple time scales within the Proper Generalized Decomposition framework

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Angelo Pasquale ◽  
Amine Ammar ◽  
Antonio Falcó ◽  
Simona Perotto ◽  
Elías Cueto ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Discretization ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Proper Generalized Decomposition ◽  
Partial Differential ◽  
Time Coordinate ◽  
Separated Representation ◽  
The Time Domain ◽  
Fine Time

AbstractSolutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

scholarly journals A multistate model incorporating estimation of excess hazards and multiple time scales

2021 ◽  
Vol 40 (9) ◽  
pp. 2139-2154
Author(s):  
Caroline E. Weibull ◽  
Paul C. Lambert ◽  
Sandra Eloranta ◽  
Therese M. L. Andersson ◽  
Paul W. Dickman ◽  
...  
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multistate Model

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

scholarly journals Release of a single neurotransmitter from an identified interneuron coherently affects motor output on multiple time scales

2013 ◽  
Vol 109 (9) ◽  
pp. 2327-2334 ◽  
Author(s):  
Andrew M. Dacks ◽  
Klaudiusz R. Weiss
Keyword(s):  
Time Scales ◽  
Motor Program ◽  
Gaba Release ◽  
Motor Output ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Intrinsic Properties ◽  
Buccal Ganglion ◽  
Motor Programs ◽  
Pattern Characteristic

Neurotransmitters can have diverse effects that occur over multiple time scales often making the consequences of neurotransmission difficult to predict. To explore the consequences of this diversity, we used the buccal ganglion of Aplysia to examine the effects of GABA release by a single interneuron, B40, on the intrinsic properties and motor output of the radula closure neuron B8. B40 induces a picrotoxin-sensitive fast IPSP lasting milliseconds in B8 and a slow EPSP lasting seconds. We found that the excitatory effects of this slow EPSP are also mediated by GABA. Together, these two GABAergic actions structure B8 firing in a pattern characteristic of ingestive programs. Furthermore, we found that repeated B40 stimulation induces a persistent increase in B8 excitability that was occluded in the presence of the GABA B receptor agonist baclofen, suggesting that GABA affects B8 excitability over multiple time scales. The phasing of B8 activity during the feeding motor programs determines the nature of the behavior elicited during that motor program. The persistent increase in B8 excitability induced by B40 biased the activity of B8 during feeding motor programs causing the motor programs to become more ingestive in nature. Thus, a single transmitter released from a single interneuron can have consequences for motor output that are expressed over multiple time scales. Importantly, despite the differences in their signs and temporal characteristics, the three actions of B40 are coherent in that they promote B8 firing patterns that are characteristic of ingestive motor outputs.

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