scholarly journals Large scale singularly perturbed boundary value problems

1989 ◽  
Vol 2 (3) ◽  
pp. 139-167
Author(s):  
M. Kathirkamanayagan ◽  
G. S. Ladde
Keyword(s):  
Large Scale ◽  
Original System ◽  
Singularly Perturbed ◽  
Multiple Time Scales ◽  
Diagonal Form ◽  
Multiple Time ◽  
Modern Technique ◽  
Alternative Approach ◽  
Decomposition Processes ◽  
Singular Transformation

In this paper an alternative approach to the method of asymptotic expansions for the study of a singularly perturbed linear system with multiparameters and multiple time scales is developed. The method consists of developing a linear non-singular transformation that transforms an arbitrary n—time scale system into a diagonal form. Furthermore, a dichotomy transformation is employed to decompose the faster subsystems into stable and unstable modes. Fast, slow, stable and unstable modes decomposition processes provide a modern technique to find an approximate solution of the original system in terms of the solution of an auxiliary system. This method yields a constructive and computationally attractive way to investigate the system.

scholarly journals On the multiple time scales of variability in the Northeast Pacific Ocean

Ocean Science ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 591-605
Author(s):  
R. Tokmakian
Keyword(s):  
Pacific Ocean ◽  
Large Scale ◽  
Southern Oscillation ◽  
Set Covering ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Data Set ◽  
Northeast Pacific ◽  
Energy Signal ◽  
Northeast Pacific Ocean

Abstract. The spatial and temporal sea surface height energy distribution of the Northeast Pacific Ocean is described and discussed. Using an altimetric data set covering 15 years (1993–2007), the energy within the 3–9 month band is primarily located within 10° of the coast. In the Gulf of Alaska, this energy signal is on the shelf, while further south, west of the California/Oregon coast, the significant energy in this band is west of the shelf break. In both cases, it is primarily forced by the local wind. Within the 2–3 year band, the signal reflects energy generated by local changes to the wind stress from large atmospheric shifts indicated by the Pacific North American Index and by advective or propagating processes related to El Niño-Southern Oscillation. Over the two 4–6 year periods within this data set, the change is primarily due to the large scale shift in atmospheric systems north of about 30° N which also affect changes in current strengths. Based on the distribution of the energy signal and its variability, a set of three winter-time indices are suggested to characterize the distinct differences in the SSH anomalies in these areas.

scholarly journals An Assessment of GCM Skill in Simulating Persistence across Multiple Time Scales

2011 ◽  
Vol 24 (14) ◽  
pp. 3609-3623 ◽  
Author(s):  
Fiona Johnson ◽  
Seth Westra ◽  
Ashish Sharma ◽  
Andrew J. Pitman
Keyword(s):  
Interannual Variability ◽  
General Circulation ◽  
Large Scale ◽  
Low Frequency ◽  
General Circulation Models ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Max Planck ◽  
Reservoir Storage ◽  
Low Frequency Variability

Abstract Climate change impact studies for water resource applications, such as the development of projections of reservoir yields or the assessment of likely frequency and amplitude of drought under a future climate, require that the year-to-year persistence in a range of hydrological variables such as catchment average rainfall be properly represented. This persistence is often attributable to low-frequency variability in the global sea surface temperature (SST) field and other large-scale climate variables through a complex sequence of teleconnections. To evaluate the capacity of general circulation models (GCMs) to accurately represent this low-frequency variability, a set of wavelet-based skill measures has been developed to compare GCM performance in representing interannual variability with the observed global SST data, as well as to assess the extent to which this variability is imparted in precipitation and surface pressure anomaly fields. A validation of the derived skill measures is performed using GCM precipitation as an input in a reservoir storage context, with the accuracy of reservoir storage estimates shown to be improved by using GCM outputs that correctly represent the observed low-frequency variability. Significant differences in the performance of different GCMs is demonstrated, suggesting that judicious selection of models is required if the climate impact assessment is sensitive to low-frequency variability. The two GCMs that were found to exhibit the most appropriate representation of global low-frequency variability for individual variables assessed were the Istituto Nazionale di Geofisica e Vulcanologia (INGV) ECHAM4 and L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4); when considering all three variables, the Max Planck Institute (MPI) ECHAM5 performed well. Importantly, models that represented interannual variability well for SST also performed well for the other two variables, while models that performed poorly for SST also had consistently low skill across the remaining variables.

Cyber physics system: a review

2018 ◽  
Vol 38 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Changbin Jiang ◽  
Ying Ma ◽  
Hong Chen ◽  
Yangyin Zheng ◽  
Shan Gao ◽  
...  
Keyword(s):  
Large Scale ◽  
Research Area ◽  
Smart Manufacturing ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Medical Systems ◽  
Daily Lives ◽  
Content Type ◽  
Control Circuits

Purpose Cyber physical system (CPS) has attracted much attention from industry, government and academia due to its dramatic impact on society, economy and people’s daily lives. Scholars have conducted a number of studies on CPS. However, despite of the dynamic nature of this research area, a systematic and extensive review of recent research on CPS is unavailable. Accordingly, this paper conducts an intensive literature review on CPS and presents an overview of existing research on CPS. The purpose of this paper is to identify the challenges of studying CPS as well as the directions for future studies on CPS. Design/methodology/approach This paper examines existing literatures about CPS from 2006 to 2018 in Compendex, presenting its definition, architectures, characteristics and applications. Findings This study finds that CPS is closely integrated, diversified and large-scale network with complex multiple time scales. It requires dynamic reorganization/reconfiguration, mass computing, and closed, automated and control circuits. Currently, CPS has been applied in smart manufacturing, medical systems, smart city and smart libraries. The main challenges in designing CPS are to develop, to modify, to integrate abstractions and to set predictable timing of openness and physical interconnection of physical devices. Furthermore, security is a key issue in CPS. Originality/value This study adds knowledge to the existing literature of CPS by answering what the current level of development on CPS is and what the potential future research directions of CPS are.

scholarly journals Unsupervised detection of cell-assembly sequences with edit similarity score

2017 ◽  
Author(s):  
Keita Watanabe ◽  
Tatsuya Haga ◽  
David R Euston ◽  
Masami Tatsuno ◽  
Tomoki Fukai
Keyword(s):  
Large Scale ◽  
Clustering Algorithms ◽  
Spike Timing ◽  
Neural Population ◽  
Multiple Time Scales ◽  
Cell Assembly ◽  
Multiple Time ◽  
Mathematical Methods ◽  
Population Activity ◽  
Assembly Sequences

SUMMARYCell assembly is a hypothetical functional unit of information processing in the brain. While technologies for recording large-scale neural activity have been advanced, mathematical methods to analyze sequential activity patterns of cell-assembly are severely limited. Here, we propose a method to extract cell-assembly sequences repeated at multiple time scales and various precisions from irregular neural population activity. The key technology is to combine “edit similarity” in computer science with machine-learning clustering algorithms, where the former defines a “distance” between two strings as the minimal number of operations required to transform one string to the other. Our method requires no external references for pattern detection, and is tolerant of spike timing jitters and length irregularity in assembly sequences. These virtues enabled simultaneous automatic detections of hippocampal place-cell sequences during locomotion and their time-compressed replays during resting states. Furthermore, our method revealed previously undetected cell-assembly structure in the rat prefrontal cortex during goal-directed behavior. Thus, our method expands the horizon of cell-assembly analysis.

Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays

2004 ◽  
Vol 126 (3) ◽  
pp. 462-466 ◽  
Author(s):  
Shing-Tai Pan ◽  
Ching-Fa Chen ◽  
Jer-Guang Hsieh
Keyword(s):  
Asymptotic Stability ◽  
Time Delays ◽  
Original System ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Fast Subsystem ◽  
Multiple Time Delays ◽  
Perturbed Systems ◽  
Slow Subsystem

The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent and ε-independent, are then proposed in terms of the H∞-norm for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound ε* of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any ε∈0,ε*. Two numerical examples are provided to illustrate the use of our main results.

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