scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

scholarly journals Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

scholarly journals Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

2021 ◽  
Author(s):  
Jill Marie Anderson Padgett
Keyword(s):  
Numerical Solution ◽  
Master Equation ◽  
Reaction Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Cellular Processes ◽  
Time Stepping ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
And Diffusion ◽  
Adaptive Time Stepping

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.

scholarly journals An efficient implicit‐explicit adaptive time stepping scheme for multiple‐time scale problems in shear zone development

2013 ◽  
Vol 14 (9) ◽  
pp. 3462-3478 ◽  
Author(s):  
Byung‐Dal So ◽  
David A. Yuen ◽  
Sang‐Mook Lee
Keyword(s):  
Shear Zone ◽  
Time Scale ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Time Stepping ◽  
Adaptive Time ◽  
Zone Development ◽  
Adaptive Time Stepping

scholarly journals Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

2021 ◽  
Author(s):  
Jill Marie Anderson Padgett
Keyword(s):  
Numerical Solution ◽  
Master Equation ◽  
Reaction Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Cellular Processes ◽  
Time Stepping ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
And Diffusion ◽  
Adaptive Time Stepping

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.

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

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

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