A time-dependent PDE regularization to model functional data defined over spatio-temporal domains

2017 ◽  
pp. 41-44
Author(s):  
Eleonora Arnone ◽  
Laura Azzimonti ◽  
Fabio Nobile ◽  
Laura M. Sangalli
Keyword(s):  
Functional Data ◽  
Time Dependent ◽  
Spatio Temporal

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.

scholarly journals Investigating fine-scale spatio-temporal predator-prey patterns in dynamic marine ecosystems: a functional data analysis approach

2012 ◽  
Vol 49 (2) ◽  
pp. 481-492 ◽  
Author(s):  
Clare B. Embling ◽  
Janine Illian ◽  
Eric Armstrong ◽  
Jeroen van der Kooij ◽  
Jonathan Sharples ◽  
...  
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Marine Ecosystems ◽  
Analysis Approach ◽  
Fine Scale ◽  
Predator Prey ◽  
Spatio Temporal

scholarly journals Spatio-Temporal Clustering of Time-Dependent Origin-Destination Electronic Trace Data

2018 ◽  
Vol 130 ◽  
pp. 359-367
Author(s):  
Daphne van Leeuwen ◽  
Joost Bosman ◽  
Elenna Dugundji
Keyword(s):  
Time Dependent ◽  
Trace Data ◽  
Temporal Clustering ◽  
Spatio Temporal

The RC Analogy Provides a Versatile Computational Tool for Unsteady, Unidirectional Heat Conduction in Regular Solid Bodies Cooled by Adjoining Fluids

2003 ◽  
Vol 31 (3) ◽  
pp. 233-244
Author(s):  
Antonio Campo ◽  
Francisco Alhama
Keyword(s):  
Heat Transfer ◽  
Initial Conditions ◽  
Simulation Method ◽  
Heat Fluxes ◽  
Total Heat ◽  
Time Dependent ◽  
Total Heat Transfer ◽  
Transfer Rates ◽  
Electric Circuits ◽  
Spatio Temporal

Evaluation of spatio-temporal temperatures and total heat transfer rates in simple bodies (large plate, long cylinder and sphere) has been traditionally explained in undergraduate courses of heat transfer by the Heisler/Gröber or by the Boelter/Gröber charts. These three charts pose some restrictions with respect to the applicable times. Additionally, the charts do not provide information about the time-dependent heat fluxes at the surface. Conversely, evaluation of spatio-temporal temperatures, time-dependent heat fluxes at the surface and total heat transfer rates can be easily done for the entire time domain with the network simulation method (NSM) in conjunction with the commercial code PSPICE. NSM relies on the existing physical analogy between the unsteady transport of electric current and the unsteady transport of unidirectional heat by conduction. This analogy has been named the RC analogy in the specialized literature. The code PSPICE simulates the electric circuits for a specific body together with the imposed boundary and initial conditions, and produces numerical results for the quantities of interest, such as: the spatio-temporal temperature distributions; the time-dependent heat flux distributions at the surface; and the total heat transfer.

scholarly journals Frictional Heating with Time-Dependent Specific Power of Friction

2017 ◽  
Vol 11 (2) ◽  
pp. 111-115 ◽  
Author(s):  
Katarzyna Topczewska
Keyword(s):  
Time Distribution ◽  
Frictional Heating ◽  
Heat Fluxes ◽  
Time Dependent ◽  
Frictional Heat ◽  
Specific Power ◽  
Dimensionless Temperature ◽  
Brake Disc ◽  
Dimensionless Form ◽  
Spatio Temporal

AbstractIn this paper analytical solutions of the thermal problems of friction were received. The appropriate boundary-value problems of heat conduction were formulated and solved for a homogeneous semi–space (a brake disc) heated on its free surface by frictional heat fluxes with different and time-dependent intensities. Solutions were obtained in dimensionless form using Duhamel's theorem. Based on received solutions, evolution and spatial distribution of the dimensionless temperature were analyzed using numerical methods. The numerical results allowed to determine influence of the time distribution of friction power on the spatio-temporal temperature distribution in brake disc.

scholarly journals Time-Dependent Image Restoration of Low-SNR Live-Cell Ca2 Fluorescence Microscopy Data

2021 ◽  
Vol 22 (21) ◽  
pp. 11792
Author(s):  
Lena-Marie Woelk ◽  
Sukanya A. Kannabiran  ◽  
Valerie J. Brock  ◽  
Christine E. Gee  ◽  
Christian Lohr  ◽  
...  
Keyword(s):  
Fluorescence Microscopy ◽  
Image Restoration ◽  
Signal To Noise Ratio ◽  
Synthetic Data ◽  
Image Data ◽  
Live Cell ◽  
Time Dependent ◽  
Temporal Consistency ◽  
Spatio Temporal ◽  
Microscopy Data

Live-cell Ca2+ fluorescence microscopy is a cornerstone of cellular signaling analysis and imaging. The demand for high spatial and temporal imaging resolution is, however, intrinsically linked to a low signal-to-noise ratio (SNR) of the acquired spatio-temporal image data, which impedes on the subsequent image analysis. Advanced deconvolution and image restoration algorithms can partly mitigate the corresponding problems but are usually defined only for static images. Frame-by-frame application to spatio-temporal image data neglects inter-frame contextual relationships and temporal consistency of the imaged biological processes. Here, we propose a variational approach to time-dependent image restoration built on entropy-based regularization specifically suited to process low- and lowest-SNR fluorescence microscopy data. The advantage of the presented approach is demonstrated by means of four datasets: synthetic data for in-depth evaluation of the algorithm behavior; two datasets acquired for analysis of initial Ca2+ microdomains in T-cells; finally, to illustrate the transferability of the methodical concept to different applications, one dataset depicting spontaneous Ca2+ signaling in jGCaMP7b-expressing astrocytes. To foster re-use and reproducibility, the source code is made publicly available.

Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional data

2019 ◽  
Vol 131 ◽  
pp. 176-193 ◽  
Author(s):  
Joshua French ◽  
Piotr Kokoszka ◽  
Stilian Stoev ◽  
Lauren Hall
Keyword(s):  
Extreme Value Theory ◽  
Functional Data ◽  
Heat Waves ◽  
Value Theory ◽  
Extreme Value ◽  
Spatio Temporal
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