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Modelling With The Master Equation


Modelling With The Master Equation
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Modelling With The Master Equation


Modelling With The Master Equation
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Author : Günter Haag
language : en
Publisher: Springer
Release Date : 2017-07-31

Modelling With The Master Equation written by Günter Haag and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 with Social Science categories.


This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.



Master Equation Models Of Macromolecular Dynamics From Atomistic Simulation


Master Equation Models Of Macromolecular Dynamics From Atomistic Simulation
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Author : John D. Chodera
language : en
Publisher:
Release Date : 2006

Master Equation Models Of Macromolecular Dynamics From Atomistic Simulation written by John D. Chodera and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.


This dissertation is concerned with the construction, validation, and use of master equation models for the study of macromolecular conformational dynamics. The master equation formalism is a powerful tool for describing the dynamics of a system that can be characterized by a discrete-state, continuous-time Markov process. Once constructed from a large quantities of short trajectories, the evolution of experimentally measurable dynamical observables can be computed and compared with experiment. Additionally, information not yet directly accessible to experiment but which may be useful in aiding understanding or the generation of novel hypotheses, such as folding pathways, transiently populated conformations, and mean first passage times, can also be easily obtained. We demonstrate that a master equation model constructed from short trajectories can describe slow conformational dynamics for a solvated alanine peptide over long times, propose a number of tests to tell whether a model constructed from short trajectories will adequately describe dynamics over long times, and describe an algorithm for the automatic construction of these models from simulation data. While the focus here is on protein folding and dynamics, these techniques are very general, and can be broadly applied to problems in biomolecular dynamics.



On Reduced Models For The Chemical Master Equation


On Reduced Models For The Chemical Master Equation
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Author : Tobias Jahnke
language : en
Publisher:
Release Date : 2011

On Reduced Models For The Chemical Master Equation written by Tobias Jahnke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.




Chemical Master Equation For Large Biological Networks


Chemical Master Equation For Large Biological Networks
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Author : Don Kulasiri
language : en
Publisher: Springer Nature
Release Date : 2021-09-12

Chemical Master Equation For Large Biological Networks written by Don Kulasiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-12 with Science categories.


This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.



Modelling Single Molecule Single Photon Sources Using Master Equation


Modelling Single Molecule Single Photon Sources Using Master Equation
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Author : Ramazan Uzel
language : en
Publisher:
Release Date : 2011

Modelling Single Molecule Single Photon Sources Using Master Equation written by Ramazan Uzel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Equations categories.




Master Equation Modelling Of Energy Transport In Biomolecules


Master Equation Modelling Of Energy Transport In Biomolecules
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Author : Luis Valiño Borau
language : en
Publisher:
Release Date : 2021

Master Equation Modelling Of Energy Transport In Biomolecules written by Luis Valiño Borau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Biomolecules categories.




Solving Heterogeneous Agent Models With The Master Equation


Solving Heterogeneous Agent Models With The Master Equation
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Author : Adrien Bilal
language : en
Publisher:
Release Date : 2023

Solving Heterogeneous Agent Models With The Master Equation written by Adrien Bilal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.


This paper proposes an analytic representation of perturbations in heterogeneous agent economies with aggregate shocks. Treating the underlying distribution as an explicit state variable, a single value function defined on an infinite-dimensional state space provides a fully recursive representation of the economy: the 'Master Equation' introduced in the mathematics mean field games literature. I show that analytic local perturbations of the Master Equation around steady-state deliver dramatic simplifications. The First-order Approximation to the Master Equation (FAME) reduces to a standard Bellman equation for the directional derivatives of the value function with respect to the distribution and aggregate shocks. The FAME has six main advantages: (i) finite dimension; (ii) closed-form mapping to steady-state objects; (iii) applicability when many distributional moments or prices enter individuals' decision such as dynamic trade, urban or job ladder settings; (iv) block-recursivity bypassing further fixed points; (v) mapping to analytic sequence-space derivatives; (vi) fast implementation using standard numerical methods. I develop the Second-order Approximation to the Master Equation (SAME) and show that it shares these properties, making the approach amenable to settings such as asset pricing. I apply the method to two economies: an incomplete market model with unemployment and a wage ladder, and a discrete choice spatial model with migration.



Unified Einstein Virasoro Master Equation In The General Non Linear Sigma Model


Unified Einstein Virasoro Master Equation In The General Non Linear Sigma Model
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Author :
language : en
Publisher:
Release Date : 1996

Unified Einstein Virasoro Master Equation In The General Non Linear Sigma Model written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.


The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^abJ_aJ_b+iD^a \dif J_a$ in the operator algebra of the WZW model, where $L^ab$ is the inverse inertia tensor and $D^a $ is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field $L^ab$ to the background fields of the sigma model. For a particular solution $L_G^ab$, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its relation to an unsolved problem in the theory of $G$-structures on manifolds with torsion.



Mathematical Models Of Chemical Reactions


Mathematical Models Of Chemical Reactions
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Author : Péter Érdi
language : en
Publisher: Manchester University Press
Release Date : 1989

Mathematical Models Of Chemical Reactions written by Péter Érdi and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Chemical reactions categories.




Master Equation Modeling Of A Nanosecond Pulsed Discharge In Nitrogen In Pin To Pin Geometry


Master Equation Modeling Of A Nanosecond Pulsed Discharge In Nitrogen In Pin To Pin Geometry
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Author : Zakari Eckert
language : en
Publisher:
Release Date : 2015

Master Equation Modeling Of A Nanosecond Pulsed Discharge In Nitrogen In Pin To Pin Geometry written by Zakari Eckert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.


In this thesis, a kinetic model for a nanosecond pulsed discharge in nitrogen is presented. The model is based on nonPDPSIM, a plasma dynamics and kinetics model developed by Dr. Mark Kushner at the University of Michigan. The development of such a model is motivated by the need for a predictive design and analysis tool for applications such as plasma assisted combustion, plasma flow control, plasma medicine, and plasma materials processing. A fundamental understanding of plasma dynamics and non-equilibrium energy coupling would allow further development of these technologies, leading to better efficiency and effectiveness. More specifically, in strongly non-equilibrium plasmas the effects of anharmonic vibrational pumping can lead to high populations of high vibrational levels of diatomic gases, such as N2 , the focus of this work. Vibrationally excited molecules may store a large fraction of the coupled discharge energy and accelerate chemical reactions. Used as a baseline model, nonPDPSIM is a finite volume unstructured solver including a Poisson equation for electric potential; species concentration equations for neutral, excited, and charged species which include species transport and chemistry; separate energy equations for the heavy species and the electrons; and a two-term expansion Boltzmann equation to predict electron impact process rates and electron swarm parameters. This thesis details modifications to nonPDPSIM, including a correction to the term calculating electron heating by the electric field, modified assumptions for ion mobility, updating of electron impact cross-sections in the Boltzmann equation solver, and the addition of a master equation for N2 vibrational level populations controlled by vibrational-vibrational, vibrational-translational, and radial diffusion processes. After these modifications, the model was used to simulate a 250 ns duration discharge pulse in 100 torr of nitrogen, along with the afterglow. Model predictions are compared with experimental current and coupled energy waveforms, ICCD images of plasma emission, relative populations of excited N2 vibrational levels, and N atom number density, measured in recent experiments. Similarities and differences between kinetic modeling predictions and experimental data are discussed, and future model development is outlined.