Computing Energy Optimal Paths in Time-Varying Flows

2016 ◽  
Author(s):  
Dhanushka N. Kularatne ◽  
Subhrajit Bhattacharya ◽  
M. Ani Hsieh
Keyword(s):  
Flow Field ◽  
Configuration Space ◽  
Search Space ◽  
Ocean Model ◽  
Graph Representation ◽  
Energy Budgets ◽  
Time Varying ◽  
Marine Vehicles ◽  
Optimal Paths ◽  
Spatio Temporal

Autonomous marine vehicles (AMVs) are typically deployed for long periods of time in the ocean to monitor different physical, chemical, and biological processes. Given their limited energy budgets, it makes sense to consider motion plans that leverage the dynamics of the surrounding flow field so as to minimize energy usage for these vehicles. In this paper, we present two graph search based methods to compute energy optimal paths for AMVs in two-dimensional (2-D) time-varying flows. The novelty of the proposed algorithms lies in a unique discrete graph representation of the 3-D configuration space spanned by the spatio-temporal coordinates. This enables a more efficient traversal through the search space, as opposed to a full search of the spatio-temporal configuration space. Furthermore, the proposed strategy results in solutions that are closer to the global optimal when compared to greedy searches through the spatial coordinates alone. We demonstrate the proposed algorithms by computing optimal energy paths around the Channel Islands in the Santa Barbara bay using time-varying flow field forecasts generated by the Regional Ocean Model System. We verify the accuracy of the computed paths by comparing them with paths computed via an optimal control formulation.

scholarly journals Spatio-temporal integration in plant tropisms

2019 ◽  
Vol 16 (154) ◽  
pp. 20190038 ◽  
Author(s):  
Yasmine Meroz ◽  
Renaud Bastien ◽  
L. Mahadevan
Keyword(s):  
Response Function ◽  
Shoot Growth ◽  
Analytic Solution ◽  
Temporal Integration ◽  
Time Varying ◽  
Local Response ◽  
History Of ◽  
Non Local ◽  
Spatio Temporal ◽  
Plant Shoots

Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse stimulus expresses the response function as a function of experimentally tractable variables, which we calculate for the case of the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging, etc.

Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays

2018 ◽  
Vol 50 (2) ◽  
pp. 1051-1064 ◽  
Author(s):  
Chengdong Yang ◽  
Tingwen Huang ◽  
Kejia Yi ◽  
Ancai Zhang ◽  
Xiangyong Chen ◽  
...  
Keyword(s):  
Multiple Time ◽  
Time Varying ◽  
Temporal Networks ◽  
Spatio Temporal ◽  
Time Invariant

Multi-modal transportation recommendation with unified route representation learning

2020 ◽  
Vol 14 (3) ◽  
pp. 342-350
Author(s):  
Hao Liu ◽  
Jindong Han ◽  
Yanjie Fu ◽  
Jingbo Zhou ◽  
Xinjiang Lu ◽  
...  
Keyword(s):  
Large Scale ◽  
Transportation Networks ◽  
Representation Learning ◽  
Transportation Systems ◽  
Graph Representation ◽  
Dynamic Graph ◽  
Arbitrary Length ◽  
Task Learning ◽  
Semantic Coherence ◽  
Spatio Temporal

Multi-modal transportation recommendation aims to provide the most appropriate travel route with various transportation modes according to certain criteria. After analyzing large-scale navigation data, we find that route representations exhibit two patterns: spatio-temporal autocorrelations within transportation networks and the semantic coherence of route sequences. However, there are few studies that consider both patterns when developing multi-modal transportation systems. To this end, in this paper, we study multi-modal transportation recommendation with unified route representation learning by exploiting both spatio-temporal dependencies in transportation networks and the semantic coherence of historical routes. Specifically, we propose to unify both dynamic graph representation learning and hierarchical multi-task learning for multi-modal transportation recommendations. Along this line, we first transform the multi-modal transportation network into time-dependent multi-view transportation graphs and propose a spatiotemporal graph neural network module to capture the spatial and temporal autocorrelation. Then, we introduce a coherent-aware attentive route representation learning module to project arbitrary-length routes into fixed-length representation vectors, with explicit modeling of route coherence from historical routes. Moreover, we develop a hierarchical multi-task learning module to differentiate route representations for different transport modes, and this is guided by the final recommendation feedback as well as multiple auxiliary tasks equipped in different network layers. Extensive experimental results on two large-scale real-world datasets demonstrate the performance of the proposed system outperforms eight baselines.

Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200003 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Autonomous Systems ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Dependent Model ◽  
Spatio Temporal

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

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