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191126t20202020enk ob 001 0 eng |
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|a 9781108628389
|q (electronic book)
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|a 1108628389
|q (electronic book)
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|z 9781108498128
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|a QA274
|b .E73 2020
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| 082 |
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|a 515/.3534
|2 23
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| 100 |
1 |
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|a Erban, Radek,
|e author.
|0 http://id.loc.gov/authorities/names/n2019023224
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| 245 |
1 |
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|a Stochastic modelling of reaction-diffusion processes /
|c Radek Erban (University of Oxford), S. Jonathan Chapman (University of Oxford).
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| 264 |
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|a Cambridge ;
|a New York, NY :
|b Cambridge University Press,
|c [2020]
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| 264 |
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|c ©2020
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| 300 |
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|a 1 online resource.
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
1 |
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|a Cambridge texts in applied mathematics
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| 504 |
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|a Includes bibliographical references and index.
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|a Online resource; title from digital title page (viewed on November 26, 2019).
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|a Cover -- Half-title page -- Series page -- Title page -- Copyright page -- Contents -- Preface -- 1 Stochastic Simulation of Chemical Reactions -- 1.1 Stochastic Simulation of Degradation -- 1.2 Stochastic Simulation of Production and Degradation -- 1.3 Higher-Order Chemical Reactions -- 1.4 Stochastic Simulation of Dimerization -- 1.5 Gillespie Algorithm -- Exercises -- 2 Deterministic versus Stochastic Modelling -- 2.1 Systems with Multiple Favourable States -- 2.2 Self-Induced Stochastic Resonance -- 2.3 Stochastic Focusing -- 2.4 Designing Stochastic Chemical Systems -- Exercises
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| 505 |
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|a 3 Stochastic Differential Equations -- 3.1 A Computational Definition of SDE -- 3.2 Examples of SDEs -- 3.3 Fokker-Planck Equation -- 3.4 Boundary Conditions on the Fokker-Planck Equation -- 3.5 Kolmogorov Backward Equation -- 3.6 SDEs with Multiple Favourable States -- 3.7 Chemical Fokker-Planck Equation -- 3.8 Analysis of Problem from Section 2.1 -- 3.9 Analysis of Problem from Section 2.2 -- Exercises -- 4 Diffusion -- 4.1 Diffusion Modelled by SDEs -- 4.2 Compartment-Based Approach to Diffusion -- 4.3 Diffusion and Velocity-Jump Processes -- 4.4 Diffusion to Adsorbing Surfaces
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|a 4.5 Reactive Boundary Conditions -- 4.6 Einstein-Smoluchowski Relation -- Exercises -- 5 Efficient Stochastic Modelling of Chemical Reactions -- 5.1 A Simple Multiscale Problem -- 5.2 Multiscale SSA with Partial Equilibrium Assumption -- 5.3 Multiscale Modelling -- 5.4 First-Reaction SSA -- 5.5 Exact Efficient SSAs -- Exercises -- 6 Stochastic Reaction-Diffusion Models -- 6.1 A Compartment-Based Reaction-Diffusion Algorithm -- 6.2 A Reaction-Diffusion SSA Based on the SDE Model of Diffusion -- 6.3 Compartment-Based SSA for Higher-Order Reactions -- 6.4 A Choice of Compartment Size h
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| 505 |
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|a 6.5 Molecular-Based Approaches for Second-Order Reactions -- 6.6 Reaction Radius and Reaction Probability -- 6.7 Modelling Reversible Reactions -- 6.8 Biological Pattern Formation -- Exercises -- 7 SSAs for Reaction-Diffusion-Advection Processes -- 7.1 SSAs for Diffusion-Advection Processes -- 7.2 Reaction-Diffusion-Advection SSAs -- 7.3 Bacterial Chemotaxis -- 7.4 Collective Behaviour of Locusts -- 7.5 Ions and Ion Channels -- 7.6 Metropolis-Hastings Algorithm -- Exercises -- 8 Microscopic Models of Brownian Motion -- 8.1 One-Particle Solvent Model -- 8.2 Generalized Langevin Equation
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| 505 |
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|a 8.3 Solvent as Harmonic Oscillators -- 8.4 Solvent as Points Colliding with the Diffusing Particle -- 8.5 Forces Between Atoms and Molecules -- 8.6 Molecular Dynamics -- Exercises -- 9 Multiscale and Multi-Resolution Methods -- 9.1 Coupling SDE-Based and Compartment-Based Models -- 9.2 Coupling Molecular Dynamics with Langevin Dynamics -- 9.3 Multi-Resolution Molecular and Brownian Dynamics -- Exercises -- Appendix -- Appendix A Deterministic Modelling of Chemical Reactions -- Appendix B Discrete Probability Distributions -- Appendix C Continuous Probability Distributions -- References -- Index
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| 500 |
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|a Electronic resource.
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| 650 |
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|a Stochastic processes
|v Textbooks.
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| 650 |
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|a Reaction-diffusion equations
|v Textbooks.
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| 655 |
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7 |
|a Electronic books.
|2 local
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| 700 |
1 |
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|a Chapman, Jon,
|e author.
|0 http://id.loc.gov/authorities/names/nb2012001371
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| 710 |
2 |
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|a Cambridge University Press.
|0 http://id.loc.gov/authorities/names/n50059133
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| 830 |
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0 |
|a Cambridge texts in applied mathematics.
|0 http://id.loc.gov/authorities/names/n86719346
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| 856 |
4 |
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|u http://proxy.library.tamu.edu/login?url=https://doi.org/10.1017/9781108628389
|z Connect to the full text of this electronic book
|t 0
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|a machinegen
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| 952 |
f |
f |
|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e QA274 .E73 2020
|h Library of Congress classification
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| 998 |
f |
f |
|a QA274 .E73 2020
|t 0
|l Available Online
|