The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation

2014 ◽  
Vol 141 (6) ◽  
pp. 065102 ◽  
Author(s):  
Luciana Renata de Oliveira ◽  
Armando Bazzani ◽  
Enrico Giampieri ◽  
Gastone C. Castellani
2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Rahul Kosarwal ◽  
Don Kulasiri ◽  
Sandhya Samarasinghe

Abstract Background Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.


A new qualitative conception of the detonation mechanism in condensed explosives has been developed on the basis of experimental and numerical modelling data. According to the conception the mechanism consists of two stages: non-equilibrium and equilibrium. The mechanism regularities are explosive characteristics and they do not depend on explosive charge structure (particle size, nature of filler in the pores, explosive state, liquid or solid, and so on). The tremendous rate of loading inside the detonation wave shock discontinuity zone ( ca. 10 -13 s) is responsible for the origin of the non-equilibrium stage. For this reason, the kinetic part of the shock compression energy is initially absorbed only by the translational degrees of freedom of the explosive molecules. It involves the appearance of extremely high translational temperatures for the polyatomic molecules. In the course of the translational-vibrational relaxation processes (that is, during the first non-equilibrium stage of ca. 10 -10 s time duration) the most rapidly excited vibrational degrees of freedom can accumulate surplus energy, and the corresponding bonds decompose faster than behind the front at the equilibrium stage. In addition to this process, the explosive molecules become electronically excited and thermal ionization becomes possible inside the translational temperature overheat zone. The molecules thermal decomposition as well as their electronic excitation and thermal ionization result in some active particles (radicals, ions) being created. The active particles and excited molecules govern the explosive detonation decomposition process behind the shock front during the second equilibrium stage. The activation energy is usually low, so that during this stage the decomposition proceeds extremely rapidly. Therefore the experimentally observed dependence of the detonation decomposition time for condensed explosives is rather weak.


2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.


2021 ◽  
Author(s):  
Farida Ansari

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.


2010 ◽  
Vol 4 (1) ◽  
Author(s):  
Verena Wolf ◽  
Rushil Goel ◽  
Maria Mateescu ◽  
Thomas A Henzinger

2013 ◽  
Vol 102 (6) ◽  
pp. 67003
Author(s):  
Jia Wang ◽  
Yue Yang ◽  
Yao Yao ◽  
Chang-Qin Wu

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