scholarly journals Compartor: a toolbox for the automatic generation of moment equations for dynamic compartment populations

2021 ◽  
Author(s):  
Tobias Pietzsch ◽  
Lorenzo Duso ◽  
Christoph Zechner
Keyword(s):  
Stochastic Dynamics ◽  
Moment Equation ◽  
Automatic Generation ◽  
Moment Equations ◽  
Biochemical System ◽  
Biochemical Processes ◽  
Stochastic Population Models ◽  
Living Organisms ◽  
The Moment ◽  
Python Package

Abstract Summary Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community. Availability and implementation Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

A Generalized Integral Computation Technique for Nonequilibrium Compressible Turbulent Boundary Layers Using Moment Equations

1972 ◽  
Vol 39 (3) ◽  
pp. 667-672 ◽  
Author(s):  
J. P. Lamb ◽  
L. J. Hesler ◽  
J. H. Smith
Keyword(s):  
Boundary Layers ◽  
Mechanical Energy ◽  
Moment Equation ◽  
Turbulent Boundary Layers ◽  
Moment Equations ◽  
Governing Equations ◽  
Starting Conditions ◽  
The Moment ◽  
Momentum Integral ◽  
Layer Concept

Computation of nonequilibrium compressible turbulent boundary layers using Coles’ three-parameter representation for the layer (cf, δ, Π) is discussed. Governing equations include momentum integral, skin friction, and an integral moment equation. It is shown that the hypothetical equilibrium layer concept employed by Alber to determine the dissipation integral of the mechanical energy equation can be utilized to estimate similar auxiliary parameters in the entrainment and moment-of-momentum integral equations. A series of comparisons of experimental data and predictions, using each of the moment equations shows that all combinations yield very similar results which are in general agreement with measurements. Some sensitivity to starting conditions was observed with the moment-of-momentum and entrainment relations.

Evaluation of moment equation in the 2000 Canadian highway bridge design code for soil–metal arch structures

2004 ◽  
Vol 31 (2) ◽  
pp. 281-291 ◽  
Author(s):  
Dong-Ho Choi ◽  
Gi-Nam Kim ◽  
Peter M Byrne
Keyword(s):  
Finite Element ◽  
Moment Equation ◽  
Finite Element Analyses ◽  
Moment Equations ◽  
Metal Structures ◽  
Maximum Moment ◽  
Design Variables ◽  
Arch Structures ◽  
The Moment ◽  
Soil Metal

This paper evaluates the moment equation in the 2000 Canadian highway bridge design code (CHBDC) for soil–metal arch structures. This equation is adopted from Duncan's moment equation (1978), which is based on his finding from finite element analyses that the maximum moment occurs at the quarter point of soil-metal structures. However, finite element analyses carried out for this study demonstrate that the maximum moment in soil–metal arch structures with spans greater than approximately 11 m occurs at the crown point. In this study, the location and magnitude of the maximum moment was examined for soil–metal arch structures having spans of 6–20 m under three construction stages; backfill up to the crown, backfill up to the cover depth, and live loading. Based on the location of the maximum moment, two sets of moment equations dependant on span length were found necessary. Moment coefficients and moment reduction factors in moment equations are proposed from the results of numerous finite element analyses for semi-circular arch and part-arch types of soil–metal structures considering the various design variables, such as span length, structural shapes, section properties, and backfill conditions. The validity of the coefficients and reduction factors in the moment equation of the 2000 CHBDC is investigated by comparison with those proposed in this study. The comparison demonstrates that the moment equation of the 2000 CHBDC is still valid and a little conservative. The effects of design variables on the variations of moments of soil–metal arch structures during construction stages are also examined.Key words: soil–metal arch structures, moment equations, CHBDC, soil-structure interaction.

Application of a High-Order Macroscopic Approach to Force-Driven Poiseuille Flow in the Slip and Transition Regimes

2008 ◽  
Author(s):  
Simon Mizzi ◽  
Xiao-Jun Gu ◽  
David R. Emerson ◽  
Robert W. Barber ◽  
Jason M. Reese
Keyword(s):  
Boundary Conditions ◽  
Poiseuille Flow ◽  
Solid Wall ◽  
Moment Equation ◽  
Moment Equations ◽  
Molecular Collision ◽  
Macroscopic Models ◽  
Gaseous Flows ◽  
Wall Interaction ◽  
The Moment

In this paper various extended macroscopic models are described and applied to force-driven Poiseuille flow. In particular, details are given for the regularized Grad 13- and 20-moment equations. Extended macroscopic models have, until recently, been limited by the uncertainity surrounding the prescription of boundary conditions on solid-walls. The gas-solid wall interaction plays an important role in describing the dynamics of confined gaseous flows. This problem is tackled in the context of the moment equations whereby the simplified Maxwell microscopic formalism is used to derive boundary conditions for a given moment equation set. The proposed governing equations and boundary conditions are applied to force-driven Poiseuille flow where anomalous thermal behavior is observed as the Knudsen number increases. Results are compared to DSMC data and it is established that the proposed extended macroscopic models can capture this non-intuitive behavior. However, the models show some quantitative disparity in representing this behavior. It is proposed that this is addressed by development of a consistent theory of molecular collision geometries in the extended hydro-dynamic model or by the utilization of more extended moment sets.

scholarly journals Neural network aided approximation and parameter inference of non-Markovian models of gene expression

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingchao Jiang ◽  
Xiaoming Fu ◽  
Shifu Yan ◽  
Runlai Li ◽  
Wenli Du ◽  
...  
Keyword(s):  
Neural Network ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Parameter Inference ◽  
Biochemical Processes ◽  
Markovian Models ◽  
The Neural Network ◽  
Large Numbers ◽  
Small Set ◽  
Noisy Measurements

AbstractNon-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

The moment equations for three-group systems

1981 ◽  
Vol 43 (1) ◽  
pp. 40-48
Author(s):  
P.L Corio ◽  
M.L Trover
Keyword(s):  
Moment Equations ◽  
The Moment

Electromagnetic wave backscattering across a magnetic field in a bounded plasma

1979 ◽  
Vol 22 (1) ◽  
pp. 85-96
Author(s):  
Joseph E. Willett ◽  
Sinan Bilikmen ◽  
Behrooz Maraghechi
Keyword(s):  
Magnetic Field ◽  
Numerical Study ◽  
Magnetized Plasma ◽  
Absolute Instability ◽  
Moment Equations ◽  
Homogeneous Plasma ◽  
Coupled Equations ◽  
Bounded Plasma ◽  
The Moment ◽  
The Magnetic Field

The stimulated backscattering of electromagnetic ordinary waves from extraordinary waves propagating normal to a magnetic field in a plasma of finite length is studied. A pair of coupled differential equations for the amplitudes of the backscattered and scatterer waves is derived from Maxwell's equations and the moment equations for an inhomogeneous magnetized plasma. Solution of the coupled equations for a homogeneous plasma yields an expression for the growth rate of the absolute instability as a function of plasma length and damping rates of the product waves. The convective regime in which only spatial amplification occurs is discussed. A numerical study of the effects of the magnetic field on Raman and Brillouin backscattering is presented.

scholarly journals A convergence study for the Laguerre expansion in the moment equation method for neoclassical transport in general toroidal plasmas

2010 ◽  
Vol 17 (8) ◽  
pp. 082510 ◽  
Author(s):  
S. Nishimura ◽  
H. Sugama ◽  
H. Maaßberg ◽  
C. D. Beidler ◽  
S. Murakami ◽  
...  
Keyword(s):  
Moment Equation ◽  
Equation Method ◽  
Laguerre Expansion ◽  
Toroidal Plasmas ◽  
Neoclassical Transport ◽  
Convergence Study ◽  
The Moment

A power moment reformulation of the Nikiforov–Uvarov method for exactly solvable systems

2016 ◽  
Vol 94 (4) ◽  
pp. 410-424
Author(s):  
Carlos R. Handy ◽  
Daniel Vrinceanu
Keyword(s):  
Closed Form ◽  
Discrete Spectrum ◽  
Asymptotic Form ◽  
Moment Equation ◽  
Wave Functions ◽  
Moment Equations ◽  
Power Moment ◽  
Exactly Solvable ◽  
Uvarov Method ◽  
Polynomial Expansions

Exactly solvable (ES) systems are those for which the full, discrete spectrum can be solved in closed form. In this work, we argue that a moment’s representation analysis can generate these closed-form expressions for the energy in a more direct and transparent manner than the popular Nikiforov–Uvarov (NU) procedure. NU analysis strips the asymptotic form of the physical states. We retain these to generate appropriate moment equations. We show how the form of these moment equations leads to closed-form energy expressions. The wave functions can then be generated as well. Our analysis is extendable to quasi-exactly solvable systems (QES; those for which a subset of the discrete spectrum can be generated in closed form). Two formulations are presented. One of these affirms that a previously developed, general, moment quantization procedure is exact for ES and QES states. This method is referred to as the orthogonal polynomial projection quantization method. It combines moment equation representations for physical states with weighted polynomial expansions (Handy and Vrinceanu. J. Phys. A: Math. Theor. 46, 135202 (2013). doi:10.1088/1751-8113/46/13/135202 ). We also show that in implementing any numerical search procedure to determine the quantum parameter regimes corresponding to ES or QES states, our procedure is more reliable (i.e., numerically stable) than using a Hill determinant formulation. We develop our formalism, demonstrate its effectiveness, and prove its equivalence to the NU approach for ES systems.

Functional calculus in strong plasma turbulence

1980 ◽  
Vol 24 (3) ◽  
pp. 489-501 ◽  
Author(s):  
Goodarz Ahmadi ◽  
Akira Hirose
Keyword(s):  
Functional Equation ◽  
Plasma Turbulence ◽  
Closure Problem ◽  
Moment Equations ◽  
Characteristic Functional ◽  
Velocity Wave ◽  
Space Characteristic ◽  
The Mean ◽  
Basic Equations ◽  
The Moment

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

scholarly journals Energy flows, metabolism and translation

2011 ◽  
Vol 366 (1580) ◽  
pp. 2949-2958 ◽  
Author(s):  
Robert Pascal ◽  
Laurent Boiteau
Keyword(s):  
Free Energy ◽  
Carbon Metabolism ◽  
Energy Levels ◽  
Self Organization ◽  
Discrete Events ◽  
Covalent Bonds ◽  
Biochemical Processes ◽  
Energy Flows ◽  
Living Organisms ◽  
Complex Chemistry

Thermodynamics provides an essential approach to understanding how living organisms survive in an organized state despite the second law. Exchanges with the environment constantly produce large amounts of entropy compensating for their own organized state. In addition to this constraint on self-organization, the free energy delivered to the system, in terms of potential, is essential to understand how a complex chemistry based on carbon has emerged. Accordingly, the amount of free energy brought about through discrete events must reach the strength needed to induce chemical changes in which covalent bonds are reorganized. The consequence of this constraint was scrutinized in relation to both the development of a carbon metabolism and that of translation. Amino acyl adenylates involved as aminoacylation intermediates of the latter process reach one of the higher free energy levels found in biochemistry, which may be informative on the range in which energy was exchanged in essential early biochemical processes. The consistency of this range with the amount of energy needed to weaken covalent bonds involving carbon may not be accidental but the consequence of the abovementioned thermodynamic constraints. This could be useful in building scenarios for the emergence and early development of translation.

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