2018 |
|
| 4. | Kumar, A B R; Ramaswamy, R Chemistry at the Nanoscale: When Every Reaction is a Discrete Event Journal Article Resonance, 23 , pp. 23-40, 2018, ISSN: 0973-712X. Abstract | Links | BibTeX | Tags: Chemical Kinetics, Gillespie’s Algorithm, Stochasticity, Synthetic Gene Oscillators @article{Kumar2018, title = {Chemistry at the Nanoscale: When Every Reaction is a Discrete Event}, author = {A B R Kumar and R Ramaswamy}, url = {https://ramramaswamy.org/papers/169.pdf}, doi = {10.1007/s12045-018-0592-4}, issn = {0973-712X}, year = {2018}, date = {2018-01-01}, journal = {Resonance}, volume = {23}, pages = {23-40}, abstract = {Traditionally the kinetics of a chemical reaction has been stud- ied as a set of coupled ordinary differential equations. The law of mass action, a tried and tested principle for reactions involving macroscopic quantities of reactants, gives rise to de- terministic equations in which the variables are species con- centrations. In recent years, though, as smaller and smaller systems ‚Äì such as an individual biological cell, say ‚Äì can be studied quantitatively, the importance of molecular discrete- ness in chemical reactions has increasingly been realized. This is particularly true when the system is far from the ‚Äòthermo- dynamic limit’ when the numbers of all reacting molecular species involved are several orders of magnitude smaller than Avogadro’s number. In such situations, each reaction has to be treated as a probabilistic ‚Äòevent’ that occurs by chance when the appropriate reactants collide. Explicitly accounting for such processes has led to the development of sophisticated statistical methods for simulation of chemical reactions, particularly those occurring at the cellular and sub-cellular level. In this article, we describe this approach, the so-called stochastic simulation algorithm, and discuss applications to study the dynamics of model regulatory networks.}, keywords = {Chemical Kinetics, Gillespie’s Algorithm, Stochasticity, Synthetic Gene Oscillators}, pubstate = {published}, tppubtype = {article} } Traditionally the kinetics of a chemical reaction has been stud- ied as a set of coupled ordinary differential equations. The law of mass action, a tried and tested principle for reactions involving macroscopic quantities of reactants, gives rise to de- terministic equations in which the variables are species con- centrations. In recent years, though, as smaller and smaller systems ‚Äì such as an individual biological cell, say ‚Äì can be studied quantitatively, the importance of molecular discrete- ness in chemical reactions has increasingly been realized. This is particularly true when the system is far from the ‚Äòthermo- dynamic limit’ when the numbers of all reacting molecular species involved are several orders of magnitude smaller than Avogadro’s number. In such situations, each reaction has to be treated as a probabilistic ‚Äòevent’ that occurs by chance when the appropriate reactants collide. Explicitly accounting for such processes has led to the development of sophisticated statistical methods for simulation of chemical reactions, particularly those occurring at the cellular and sub-cellular level. In this article, we describe this approach, the so-called stochastic simulation algorithm, and discuss applications to study the dynamics of model regulatory networks. |
2016 |
|
| 3. | Jafri, Haider Hasan; Singh, K.Brojen R; Ramaswamy, Ramakrishna Generalized synchrony of coupled stochastic processes with multiplicative noise Journal Article Physical Review E, 94 (5), pp. 1–8, 2016, ISSN: 24700053. Abstract | Links | BibTeX | Tags: Generalized Synchronization, Stochasticity @article{Jafri2016, title = {Generalized synchrony of coupled stochastic processes with multiplicative noise}, author = {Haider Hasan Jafri and K.Brojen R Singh and Ramakrishna Ramaswamy}, url = {https://ramramaswamy.org/papers/164.pdf}, doi = {10.1103/PhysRevE.94.052216}, issn = {24700053}, year = {2016}, date = {2016-01-01}, journal = {Physical Review E}, volume = {94}, number = {5}, pages = {1–8}, abstract = {textcopyright 2016 American Physical Society. We study the effect of multiplicative noise in dynamical flows arising from the coupling of stochastic processes with intrinsic noise. Situations wherein such systems arise naturally are in chemical or biological oscillators that are coupled to each other in a drive-response configuration. Above a coupling threshold we find that there is a strong correlation between the drive and the response: This is a stochastic analog of the phenomenon of generalised synchronization. Since the dynamical fluctuations are large when there is intrinsic noise, it is necessary to employ measures that are sensitive to correlations between the variables of drive and the response, the permutation entropy, or the mutual information in order to detect the transition to generalized synchrony in such systems.}, keywords = {Generalized Synchronization, Stochasticity}, pubstate = {published}, tppubtype = {article} } textcopyright 2016 American Physical Society. We study the effect of multiplicative noise in dynamical flows arising from the coupling of stochastic processes with intrinsic noise. Situations wherein such systems arise naturally are in chemical or biological oscillators that are coupled to each other in a drive-response configuration. Above a coupling threshold we find that there is a strong correlation between the drive and the response: This is a stochastic analog of the phenomenon of generalised synchronization. Since the dynamical fluctuations are large when there is intrinsic noise, it is necessary to employ measures that are sensitive to correlations between the variables of drive and the response, the permutation entropy, or the mutual information in order to detect the transition to generalized synchrony in such systems. |
1979 |
|
| 2. | R Ramaswamy, Augustin S; Rabitz, H Stochastic theory of collisions: Application to vibration–rotation inelasticity in CO–He Journal Article The Journal of Chemical Physics, 70 (5), pp. 2455–2462, 1979, ISSN: 0021-9606. Abstract | Links | BibTeX | Tags: molecular dynamics, Stochasticity @article{Ramaswamy1979, title = {Stochastic theory of collisions: Application to vibration–rotation inelasticity in CO–He}, author = {R Ramaswamy, S Augustin and H Rabitz}, url = {https://doi.org/10.1063/1.437706}, doi = {10.1063/1.437706}, issn = {0021-9606}, year = {1979}, date = {1979-03-01}, journal = {The Journal of Chemical Physics}, volume = {70}, number = {5}, pages = {2455–2462}, abstract = {Vibration–rotation inelasticity in the CO–He collision system is studied within the stochastic formulation. Cross sections are obtained for purely rotational transitions using a modified electron gas potential. Vibration–rotation cross sections have been calculated in the energy range 2200 cm−1 pubstate = {published}, tppubtype = {article} } Vibration–rotation inelasticity in the CO–He collision system is studied within the stochastic formulation. Cross sections are obtained for purely rotational transitions using a modified electron gas potential. Vibration–rotation cross sections have been calculated in the energy range 2200 cm−1<E<4000 cm−1. At the higher energy, a total of 76 molecular states are energetically accessible. A comparison with earlier results is made, and coarse graining techniques for the treatment of large problems are utilized. |
1978 |
|
| 1. | R Ramaswamy, Augustin S; Rabitz, H Stochastic theory of intramolecular energy transfer Journal Article The Journal of Chemical Physics, 69 (12), pp. 5509-5517, 1978, ISSN: 0021-9606. Abstract | Links | BibTeX | Tags: energy conservation, probability, Stochasticity @article{Ramaswamy1978, title = {Stochastic theory of intramolecular energy transfer}, author = {R Ramaswamy, S Augustin and H Rabitz}, url = {https://doi.org/10.1063/1.436544}, doi = {10.1063/1.436544}, issn = {0021-9606}, year = {1978}, date = {1978-12-15}, journal = {The Journal of Chemical Physics}, volume = {69}, number = {12}, pages = {5509-5517}, abstract = {The problem of internal energy redistribution in an isolated polyatomic molecule is treated by a stochastic theory approach. The fundamental assumption of this work is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrödinger equation by a master equation that governs the evolution of a probability distribution in the quantum levels of the molecule. No assumptions regarding the strength of the coupling are made, and the problem of energy conservation is specifically considered. A stochastic variable is introduced in order to satisfy the requirement that the total energy remain fixed. The further approximation of the master equation by a Fokker–Planck diffusion-like equation is outlined; the latter approach is particularly attractive for treating large molecules. Finally, the master‐equation theory is applied to a model problem representing a linearly constrained triatomic molecule, and the time evolution of an initially localized excitation is discussed.}, keywords = {energy conservation, probability, Stochasticity}, pubstate = {published}, tppubtype = {article} } The problem of internal energy redistribution in an isolated polyatomic molecule is treated by a stochastic theory approach. The fundamental assumption of this work is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrödinger equation by a master equation that governs the evolution of a probability distribution in the quantum levels of the molecule. No assumptions regarding the strength of the coupling are made, and the problem of energy conservation is specifically considered. A stochastic variable is introduced in order to satisfy the requirement that the total energy remain fixed. The further approximation of the master equation by a Fokker–Planck diffusion-like equation is outlined; the latter approach is particularly attractive for treating large molecules. Finally, the master‐equation theory is applied to a model problem representing a linearly constrained triatomic molecule, and the time evolution of an initially localized excitation is discussed. |