You can find below the publication list of all members of the theoretical chemistry group at ENS. For the list of each individual member, please consult their personal webpage from the Members page.
1981 |
Vibrational-Translational Energy Transfer from Highly Excited Anharmonic Oscillators Article de journal D J Nesbitt; J T Hynes Chemical Physics Letters, 82 (2), p. 252-254, 1981, (cited By 24). @article{Nesbitt1981252, title = {Vibrational-Translational Energy Transfer from Highly Excited Anharmonic Oscillators}, author = {D J Nesbitt and J T Hynes}, doi = {10.1016/0009-2614(81)85149-4}, year = {1981}, date = {1981-01-01}, journal = {Chemical Physics Letters}, volume = {82}, number = {2}, pages = {252-254}, abstract = {Model trajectory calculations reveal a simple power law behavior for anharmonic oscillator energy transfer for all bound vibrational levels. textcopyright 1981.}, note = {cited By 24}, keywords = {}, pubstate = {published}, tppubtype = {article} } Model trajectory calculations reveal a simple power law behavior for anharmonic oscillator energy transfer for all bound vibrational levels. textcopyright 1981. |
Reaction Rate Constant for the BGK Model Article de journal J T Hynes Chemical Physics Letters, 79 (2), p. 344-346, 1981, (cited By 21). @article{Hynes1981344, title = {Reaction Rate Constant for the BGK Model}, author = {J T Hynes}, doi = {10.1016/0009-2614(81)80218-7}, year = {1981}, date = {1981-01-01}, journal = {Chemical Physics Letters}, volume = {79}, number = {2}, pages = {344-346}, abstract = {The exact rate constant is found for reaction modelled as passage over a parabolic barrier subject to solvent collisions described by the BGK model. textcopyright 1981.}, note = {cited By 21}, keywords = {}, pubstate = {published}, tppubtype = {article} } The exact rate constant is found for reaction modelled as passage over a parabolic barrier subject to solvent collisions described by the BGK model. textcopyright 1981. |
A Continuum Theory for Quadrupole Relaxation of Ions in Solution Article de journal J T Hynes; P G Wolynes The Journal of Chemical Physics, 75 (1), p. 395-401, 1981, (cited By 45). @article{Hynes1981395, title = {A Continuum Theory for Quadrupole Relaxation of Ions in Solution}, author = {J T Hynes and P G Wolynes}, doi = {10.1063/1.441796}, year = {1981}, date = {1981-01-01}, journal = {The Journal of Chemical Physics}, volume = {75}, number = {1}, pages = {395-401}, abstract = {A simple continuum theory for quadrupole relaxation rates of ions in polar solvents is presented. The predicted rates agree fairly well with experimental rates determined for various ions in several solvents. The surprising success of the relatively crude continuum model is discussed and the implications for molecular theories of quadrupole relaxation are indicated. textcopyright 1981 American Institute of Physics.}, note = {cited By 45}, keywords = {}, pubstate = {published}, tppubtype = {article} } A simple continuum theory for quadrupole relaxation rates of ions in polar solvents is presented. The predicted rates agree fairly well with experimental rates determined for various ions in several solvents. The surprising success of the relatively crude continuum model is discussed and the implications for molecular theories of quadrupole relaxation are indicated. textcopyright 1981 American Institute of Physics. |
Reactive Modes in Condensed Phase Reactions Article de journal R F Grote; J T Hynes The Journal of Chemical Physics, 74 (8), p. 4465-4475, 1981, (cited By 220). @article{Grote19814465, title = {Reactive Modes in Condensed Phase Reactions}, author = {R F Grote and J T Hynes}, doi = {10.1063/1.441634}, year = {1981}, date = {1981-01-01}, journal = {The Journal of Chemical Physics}, volume = {74}, number = {8}, pages = {4465-4475}, abstract = {The rate constant k for condensed phase chemical reactions is found when a saddle point normal mode analysis holds and when the dynamic solvent forces are of the generalized Langevin type. If the reactive and nonreactive modes are uncoupled, the deviation of k from its transition state value ktst is governed by the nonadiabatic friction on the reactive mode. In the more typical case where the modes are coupled k/ktst is governed by an effective nonadiabatic reactive mode friction which completely accounts for intramode coupling. Some simple illustrations of mode coupling effects on k are given. textcopyright 1981 American Institute of Physics.}, note = {cited By 220}, keywords = {}, pubstate = {published}, tppubtype = {article} } The rate constant k for condensed phase chemical reactions is found when a saddle point normal mode analysis holds and when the dynamic solvent forces are of the generalized Langevin type. If the reactive and nonreactive modes are uncoupled, the deviation of k from its transition state value ktst is governed by the nonadiabatic friction on the reactive mode. In the more typical case where the modes are coupled k/ktst is governed by an effective nonadiabatic reactive mode friction which completely accounts for intramode coupling. Some simple illustrations of mode coupling effects on k are given. textcopyright 1981 American Institute of Physics. |
1980 |
The Stable States Picture of Chemical Reactions. I. Formulation for Rate Constants and Initial Condition Effects Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 73 (6), p. 2700-2714, 1980, (cited By 194). @article{Northrup19802700, title = {The Stable States Picture of Chemical Reactions. I. Formulation for Rate Constants and Initial Condition Effects}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.440484}, year = {1980}, date = {1980-01-01}, journal = {The Journal of Chemical Physics}, volume = {73}, number = {6}, pages = {2700-2714}, abstract = {The stable states picture (SSP) of chemical reactions is used to derive flux time correlation function (tcf) formulas for reaction rate constants. These formulas, which apply to both gas phase and condensed phase reactions, are interpreted in terms of the flux out of an internally equilibrated stable reactant and the ensuing irreversible flux into a stable product. The determination of the rate constants by dynamics in an intermediate region lying between these stable states is illustrated for a simple model of barrier crossing in liquids. Generalized rate constant expressions which hold when internal nonequilibrium in the stable states is important are derived and discussed. The SSP approach is also used to derive tcf expressions for short time initial condition effects which carry information on reactive dynamics beyond that contained in rate constants. As an illustration, it is shown how the SSP formulation provides a starting point for the resolution of primary and secondary recombination in liquid state photodissociation reactions. textcopyright 1980 American Institute of Physics.}, note = {cited By 194}, keywords = {}, pubstate = {published}, tppubtype = {article} } The stable states picture (SSP) of chemical reactions is used to derive flux time correlation function (tcf) formulas for reaction rate constants. These formulas, which apply to both gas phase and condensed phase reactions, are interpreted in terms of the flux out of an internally equilibrated stable reactant and the ensuing irreversible flux into a stable product. The determination of the rate constants by dynamics in an intermediate region lying between these stable states is illustrated for a simple model of barrier crossing in liquids. Generalized rate constant expressions which hold when internal nonequilibrium in the stable states is important are derived and discussed. The SSP approach is also used to derive tcf expressions for short time initial condition effects which carry information on reactive dynamics beyond that contained in rate constants. As an illustration, it is shown how the SSP formulation provides a starting point for the resolution of primary and secondary recombination in liquid state photodissociation reactions. textcopyright 1980 American Institute of Physics. |
The Stable States Picture of Chemical Reactions. II. Rate Constants for Condensed and Gas Phase Reaction Models Article de journal R F Grote; J T Hynes The Journal of Chemical Physics, 73 (6), p. 2715-2732, 1980, (cited By 1071). @article{Grote19802715, title = {The Stable States Picture of Chemical Reactions. II. Rate Constants for Condensed and Gas Phase Reaction Models}, author = {R F Grote and J T Hynes}, doi = {10.1063/1.440485}, year = {1980}, date = {1980-01-01}, journal = {The Journal of Chemical Physics}, volume = {73}, number = {6}, pages = {2715-2732}, abstract = {The time correlation function (tcf) formulas for rate constants $iota$ derived via the stable states picture (SSP) of chemical reactions are applied to a wide variety (a-d) of gas and solution phase reaction models, (a) For gas phase bimolecular reactions, we show that the flux tcf governing $kappa$ corresponds to standard numerical trajectory calculation methods. Alternate formulas for $kappa$ are derived which focus on saddle point surfaces, thus increasing computational efficiency. Advantages of the SSP formulas for are discussed. (b) For gas phase unimolecular reactions, simple results for $kappa$ are found in both the strong and weak coupling collision limits; the often ignored role of product stabilization is exposed for reversible isomerizations. The SSP results correct some standard weak coupling rate constant results by as much as 50%. (c) For barrier crossing reactions in solution, we evaluate $kappa$ for a generalized (nonMarkovian) Langevin description of the dynamics. For several realistic models of time dependent friction, $kappa$ differs dramatically from the popular Kramers constant friction predictions; this has important implications for the validity of transition state theory. (d) For solution reactions heavily influenced by spatial diffusion, we show that the SSP isolates short range reaction dynamics of interest and includes important barrier region effects in structural isomerizations often missed in standard descriptions. textcopyright 1980 American Institute of Physics.}, note = {cited By 1071}, keywords = {}, pubstate = {published}, tppubtype = {article} } The time correlation function (tcf) formulas for rate constants $iota$ derived via the stable states picture (SSP) of chemical reactions are applied to a wide variety (a-d) of gas and solution phase reaction models, (a) For gas phase bimolecular reactions, we show that the flux tcf governing $kappa$ corresponds to standard numerical trajectory calculation methods. Alternate formulas for $kappa$ are derived which focus on saddle point surfaces, thus increasing computational efficiency. Advantages of the SSP formulas for are discussed. (b) For gas phase unimolecular reactions, simple results for $kappa$ are found in both the strong and weak coupling collision limits; the often ignored role of product stabilization is exposed for reversible isomerizations. The SSP results correct some standard weak coupling rate constant results by as much as 50%. (c) For barrier crossing reactions in solution, we evaluate $kappa$ for a generalized (nonMarkovian) Langevin description of the dynamics. For several realistic models of time dependent friction, $kappa$ differs dramatically from the popular Kramers constant friction predictions; this has important implications for the validity of transition state theory. (d) For solution reactions heavily influenced by spatial diffusion, we show that the SSP isolates short range reaction dynamics of interest and includes important barrier region effects in structural isomerizations often missed in standard descriptions. textcopyright 1980 American Institute of Physics. |
Stochastic Trajectory Simulation of Iodine Recombination in Liquids Article de journal J T Hynes; R Kapral; G M Torrie The Journal of Chemical Physics, 72 (1), p. 177-188, 1980, (cited By 72). @article{Hynes1980177, title = {Stochastic Trajectory Simulation of Iodine Recombination in Liquids}, author = {J T Hynes and R Kapral and G M Torrie}, doi = {10.1063/1.438961}, year = {1980}, date = {1980-01-01}, journal = {The Journal of Chemical Physics}, volume = {72}, number = {1}, pages = {177-188}, abstract = {A stochastic trajectory simulation of iodine recombination in dense liquid solvents is presented. The calculations utilize a mean force potential which contains direct I-I interactions as well as solvent structure effects. Dynamical solvent effects are accounted for by a random force and friction coefficient. The time dependent probability of reaction for two initially separated radicals is determined. The choice of initial separations and atomic velocity distributions is appropriate for secondary recombination. The results of this study show the importance of including the strong direct chemical forces between the I atoms; the validity of simple diffusion equation approaches can thus be assessed. Effects due to solvent structure are quantitatively examined and are interpreted in terms of "caging" in dense fluids. The computer simulation results are also compared with the solution of the Smoluchowski equation for this problem and effects due to friction coefficient variation are discussed. textcopyright 1980 American Institute of Physics.}, note = {cited By 72}, keywords = {}, pubstate = {published}, tppubtype = {article} } A stochastic trajectory simulation of iodine recombination in dense liquid solvents is presented. The calculations utilize a mean force potential which contains direct I-I interactions as well as solvent structure effects. Dynamical solvent effects are accounted for by a random force and friction coefficient. The time dependent probability of reaction for two initially separated radicals is determined. The choice of initial separations and atomic velocity distributions is appropriate for secondary recombination. The results of this study show the importance of including the strong direct chemical forces between the I atoms; the validity of simple diffusion equation approaches can thus be assessed. Effects due to solvent structure are quantitatively examined and are interpreted in terms of "caging" in dense fluids. The computer simulation results are also compared with the solution of the Smoluchowski equation for this problem and effects due to friction coefficient variation are discussed. textcopyright 1980 American Institute of Physics. |
1979 |
Short Range Caging Effects for Reactions in Solution. I. Reaction Rate Constants and Short Range Caging Picture Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 71 (2), p. 871-883, 1979, (cited By 146). @article{Northrup1979871, title = {Short Range Caging Effects for Reactions in Solution. I. Reaction Rate Constants and Short Range Caging Picture}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.438378}, year = {1979}, date = {1979-01-01}, journal = {The Journal of Chemical Physics}, volume = {71}, number = {2}, pages = {871-883}, abstract = {The effects of short range solvent structure and short range dynamical correlations are investigated for the steady state rate constant k for solution reactions influenced by diffusion. The description is in terms of a Smoluchowski equation describing relative motion of two molecules in an outer spatial translational region, supplemented by a sink term that accounts for dynamics in an inner, reaction zone. In the outer region, solvent structural effects are included by a potential of mean force, which exhibits a short range well and barrier combination leading to "potential caging." Outer region short range dynamical correlations are included via a separation-dependent diffusion coefficient, leading to "dynamical caging" as relative motion is showed at small separations. These two short range effects are neglected in standard diffusion treatments. We find that k is only modestly influenced by the above short range effects. In order to expose short range structure and correlation influence in a more sensitive way, we formulate the short range caging picture. This information focuses on events occuring at the small separations usually implied by the term "solvent cage." At this level of description, short range effects are clearly revealed. We compare our formulation with the encounter formulation of Noyes. textcopyright 1979 American Institute of Physics.}, note = {cited By 146}, keywords = {}, pubstate = {published}, tppubtype = {article} } The effects of short range solvent structure and short range dynamical correlations are investigated for the steady state rate constant k for solution reactions influenced by diffusion. The description is in terms of a Smoluchowski equation describing relative motion of two molecules in an outer spatial translational region, supplemented by a sink term that accounts for dynamics in an inner, reaction zone. In the outer region, solvent structural effects are included by a potential of mean force, which exhibits a short range well and barrier combination leading to "potential caging." Outer region short range dynamical correlations are included via a separation-dependent diffusion coefficient, leading to "dynamical caging" as relative motion is showed at small separations. These two short range effects are neglected in standard diffusion treatments. We find that k is only modestly influenced by the above short range effects. In order to expose short range structure and correlation influence in a more sensitive way, we formulate the short range caging picture. This information focuses on events occuring at the small separations usually implied by the term "solvent cage." At this level of description, short range effects are clearly revealed. We compare our formulation with the encounter formulation of Noyes. textcopyright 1979 American Institute of Physics. |
Short Range Caging Effects for Reactions in Solution. II. Escape Probability and Time Dependent Reactivity Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 71 (2), p. 884-893, 1979, (cited By 30). @article{Northrup1979884, title = {Short Range Caging Effects for Reactions in Solution. II. Escape Probability and Time Dependent Reactivity}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.438379}, year = {1979}, date = {1979-01-01}, journal = {The Journal of Chemical Physics}, volume = {71}, number = {2}, pages = {884-893}, abstract = {Short range caging effects arising from the potential of mean force and a spatial dependence of the relative diffusion coefficient are examined for three probes of solution reactions. The escape probability that potentially reactive molecules escape each other rather than react is found to be depressed at small initial separations and enhanced at large initial separations when compared to predictions of a continuum diffusion description. Two measures of time dependent reactivity, namely the "time dependent rate constant" and the probability that initially separated members of a molecular pair remain unreacted at time t, are found to exhibit nonnegligible short range effects which can be interpreted in terms of "caging." textcopyright 1979 American Institute of Physics.}, note = {cited By 30}, keywords = {}, pubstate = {published}, tppubtype = {article} } Short range caging effects arising from the potential of mean force and a spatial dependence of the relative diffusion coefficient are examined for three probes of solution reactions. The escape probability that potentially reactive molecules escape each other rather than react is found to be depressed at small initial separations and enhanced at large initial separations when compared to predictions of a continuum diffusion description. Two measures of time dependent reactivity, namely the "time dependent rate constant" and the probability that initially separated members of a molecular pair remain unreacted at time t, are found to exhibit nonnegligible short range effects which can be interpreted in terms of "caging." textcopyright 1979 American Institute of Physics. |
Molecular Theory of Translational Diffusion: Microscopic Generalization of the Normal Velocity Boundary Condition Article de journal J T Hynes; R Kapral; M Weinberg The Journal of Chemical Physics, 70 (3), p. 1456-1466, 1979, (cited By 95). @article{Hynes19791456, title = {Molecular Theory of Translational Diffusion: Microscopic Generalization of the Normal Velocity Boundary Condition}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1063/1.437584}, year = {1979}, date = {1979-01-01}, journal = {The Journal of Chemical Physics}, volume = {70}, number = {3}, pages = {1456-1466}, abstract = {A simple molecular theory is presented for the diffusion constant D for a test hard sphere translating in a hard sphere solvent. It is argued that there is a breakdown of the applicability of hydrodynamics in the neighborhood of the test particle due to collisional effects. It is shown that, as a consequence, the traditional hydrodynamic boundary condition (BC) on the particle-solvent normal relative velocity is incorrect for molecular motion. An approximate replacement for this BC is constructed from collisional considerations. With this new BC and the usual hydrodynamic equations, D is found to have two additive contributions. The first is the microscopic, collisional Enskog diffusion constant; the second is of the hydrodynamic Stokes-Einstein form. It is shown how the standard hydrodynamic Stokes-Einstein relation for D can hold numerically to a good approximation despite the dominance of (or significant contribution to) the motion by microscopic collisional contributions. Observed trends of D with size and mass ratios which contradict the analytic Stokes-Einstein relation are reproduced. The predicted D values are compared with available results of renormalized kinetic theory and Boltzmann-level kinetic theory. High density deficiencies of the new BC are discussed. textcopyright 1979 American Institute of Physics.}, note = {cited By 95}, keywords = {}, pubstate = {published}, tppubtype = {article} } A simple molecular theory is presented for the diffusion constant D for a test hard sphere translating in a hard sphere solvent. It is argued that there is a breakdown of the applicability of hydrodynamics in the neighborhood of the test particle due to collisional effects. It is shown that, as a consequence, the traditional hydrodynamic boundary condition (BC) on the particle-solvent normal relative velocity is incorrect for molecular motion. An approximate replacement for this BC is constructed from collisional considerations. With this new BC and the usual hydrodynamic equations, D is found to have two additive contributions. The first is the microscopic, collisional Enskog diffusion constant; the second is of the hydrodynamic Stokes-Einstein form. It is shown how the standard hydrodynamic Stokes-Einstein relation for D can hold numerically to a good approximation despite the dominance of (or significant contribution to) the motion by microscopic collisional contributions. Observed trends of D with size and mass ratios which contradict the analytic Stokes-Einstein relation are reproduced. The predicted D values are compared with available results of renormalized kinetic theory and Boltzmann-level kinetic theory. High density deficiencies of the new BC are discussed. textcopyright 1979 American Institute of Physics. |
Kinetic Energy Relaxation of a Test Particle in a Dense Fluid Article de journal M Pagitsas; J T Hynes; R Kapral The Journal of Chemical Physics, 71 (11), p. 4492-4501, 1979, (cited By 6). @article{Pagitsas19794492, title = {Kinetic Energy Relaxation of a Test Particle in a Dense Fluid}, author = {M Pagitsas and J T Hynes and R Kapral}, doi = {10.1063/1.438202}, year = {1979}, date = {1979-01-01}, journal = {The Journal of Chemical Physics}, volume = {71}, number = {11}, pages = {4492-4501}, abstract = {The rate constant k$epsilon$ for the relaxation of the kinetic energy of a solute test hard sphere in a dense hard sphere solvent is studied. Microscopic boundary layer and ring kinetic theory methods are used to construct a simple expression for k$epsilon$. It is found that k $epsilon$ -1 has three additive contributions arising from (a) uncorrelated binary collisions, (b) coupling to the solvent energy density, and (c) coupling to the solvent shear modes. Thus k$epsilon$ -1 is determined by the Enskog collisional relaxation rate and the rates of the hydrodynamic flows in the solvent of heat and momentum. The competition between these effects is studied as a function of particle size and mass ratios and solvent density. The regimes examined at higher density vary from the identical solute-solvent case, where k$epsilon$ is mainly collisional with a small hydrodynamic heat flow correction, to the large, massive solute case, where k$epsilon$ is governed by solvent momentum flow according to a Stokes law type relation. textcopyright 1979 American Institute of Physics.}, note = {cited By 6}, keywords = {}, pubstate = {published}, tppubtype = {article} } The rate constant k$epsilon$ for the relaxation of the kinetic energy of a solute test hard sphere in a dense hard sphere solvent is studied. Microscopic boundary layer and ring kinetic theory methods are used to construct a simple expression for k$epsilon$. It is found that k $epsilon$ -1 has three additive contributions arising from (a) uncorrelated binary collisions, (b) coupling to the solvent energy density, and (c) coupling to the solvent shear modes. Thus k$epsilon$ -1 is determined by the Enskog collisional relaxation rate and the rates of the hydrodynamic flows in the solvent of heat and momentum. The competition between these effects is studied as a function of particle size and mass ratios and solvent density. The regimes examined at higher density vary from the identical solute-solvent case, where k$epsilon$ is mainly collisional with a small hydrodynamic heat flow correction, to the large, massive solute case, where k$epsilon$ is governed by solvent momentum flow according to a Stokes law type relation. textcopyright 1979 American Institute of Physics. |
1978 |
On the Description of Reactions in Solution Article de journal S H Northrup; J T Hynes Chemical Physics Letters, 54 (2), p. 244-247, 1978, (cited By 40). @article{Northrup1978244, title = {On the Description of Reactions in Solution}, author = {S H Northrup and J T Hynes}, doi = {10.1016/0009-2614(78)80093-1}, year = {1978}, date = {1978-01-01}, journal = {Chemical Physics Letters}, volume = {54}, number = {2}, pages = {244-247}, abstract = {A formulation for diffusion-influenced reactions in solution is given in which reactive and translational contributions are separated, steady state rate-limiting step formulations are generalized to the dynamical case and the influence of different experimental initial conditions is isolated. textcopyright 1978.}, note = {cited By 40}, keywords = {}, pubstate = {published}, tppubtype = {article} } A formulation for diffusion-influenced reactions in solution is given in which reactive and translational contributions are separated, steady state rate-limiting step formulations are generalized to the dynamical case and the influence of different experimental initial conditions is isolated. textcopyright 1978. |
On Reaction Rate Constants and Rate Kernels Article de journal S H Northrup; J T Hynes Chemical Physics Letters, 54 (2), p. 248-252, 1978, (cited By 21). @article{Northrup1978248, title = {On Reaction Rate Constants and Rate Kernels}, author = {S H Northrup and J T Hynes}, doi = {10.1016/0009-2614(78)80094-3}, year = {1978}, date = {1978-01-01}, journal = {Chemical Physics Letters}, volume = {54}, number = {2}, pages = {248-252}, abstract = {A simple model for a reversible isomerization reaction A $\leftrightharpoons$ B is used to show how rate constants and their time-dependent generalizations can be related to microscopic reactive steps and nonreactive internal dynamics (e.g., vibrational relaxation). textcopyright 1978.}, note = {cited By 21}, keywords = {}, pubstate = {published}, tppubtype = {article} } A simple model for a reversible isomerization reaction A $łeftrightharpoons$ B is used to show how rate constants and their time-dependent generalizations can be related to microscopic reactive steps and nonreactive internal dynamics (e.g., vibrational relaxation). textcopyright 1978. |
Coupling of Translational and Reactive Dynamics for a Simple Lattice Model Article de journal S H Northrup; J T Hynes Journal of Statistical Physics, 18 (1), p. 91-105, 1978, (cited By 15). @article{Northrup197891, title = {Coupling of Translational and Reactive Dynamics for a Simple Lattice Model}, author = {S H Northrup and J T Hynes}, doi = {10.1007/BF01014672}, year = {1978}, date = {1978-01-01}, journal = {Journal of Statistical Physics}, volume = {18}, number = {1}, pages = {91-105}, abstract = {The problem of the coupling of translational and reactive dynamics is investigated in terms of a simple lattice model. A master equation description including repulsive and reactive interactions is analyzed in terms of a boundary layer region and reduced to source term equations at the diffusion level. Comparison is made at this level with boundary condition approaches. textcopyright 1978 Plenum Publishing Corporation.}, note = {cited By 15}, keywords = {}, pubstate = {published}, tppubtype = {article} } The problem of the coupling of translational and reactive dynamics is investigated in terms of a simple lattice model. A master equation description including repulsive and reactive interactions is analyzed in terms of a boundary layer region and reduced to source term equations at the diffusion level. Comparison is made at this level with boundary condition approaches. textcopyright 1978 Plenum Publishing Corporation. |
Reactive Dynamics for Diffusive Barrier Crossing Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 69 (12), p. 5246-5260, 1978, (cited By 82). @article{Northrup19785246, title = {Reactive Dynamics for Diffusive Barrier Crossing}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.436578}, year = {1978}, date = {1978-01-01}, journal = {The Journal of Chemical Physics}, volume = {69}, number = {12}, pages = {5246-5260}, abstract = {A theory is presented for intramolecular reactions A$rightleftharpoons$B regarded as potential barrier crossing between two stable states A and B in the large friction limit. This limit, in which dynamics are governed by spatial diffusion in the potential, is an important example of extreme deviation from transition state theory predictions. Our theory expresses the full reaction rate constants in terms of simpler contributions: (a) the barrier rate constants and (b) the internal rate constants. The former depend solely on dynamics near the barrier top and govern the rate when stable state internal equilibrium is maintained. The latter depend solely on internal equilibration dynamics in the stable states A and B (defined away from the barrier top). The internal rate constants correct the barrier rate constants for stable state internal nonequilibrium effects. These two contributions are discussed in dynamical terms in some detail. Our theoretical rate constants are evaluated and compared with the rate constants observed by monitoring population decays obtained by direct numerical integration of the Smoluchowski equation. A simple minimum principle predicts the reaction rate constants with high accuracy at any value of the barrier height. For high barriers, our predictions approach (but are more accurate than) those of the classic approximate analysis of Kramers. For very low barriers (e.g., 1.6kBT), internal nonequilibrium effects neglected by Kramers are found by our theory to account for approximately 33% of the rate constant. textcopyright 1978 American Institute of Physics.}, note = {cited By 82}, keywords = {}, pubstate = {published}, tppubtype = {article} } A theory is presented for intramolecular reactions A$rightleftharpoons$B regarded as potential barrier crossing between two stable states A and B in the large friction limit. This limit, in which dynamics are governed by spatial diffusion in the potential, is an important example of extreme deviation from transition state theory predictions. Our theory expresses the full reaction rate constants in terms of simpler contributions: (a) the barrier rate constants and (b) the internal rate constants. The former depend solely on dynamics near the barrier top and govern the rate when stable state internal equilibrium is maintained. The latter depend solely on internal equilibration dynamics in the stable states A and B (defined away from the barrier top). The internal rate constants correct the barrier rate constants for stable state internal nonequilibrium effects. These two contributions are discussed in dynamical terms in some detail. Our theoretical rate constants are evaluated and compared with the rate constants observed by monitoring population decays obtained by direct numerical integration of the Smoluchowski equation. A simple minimum principle predicts the reaction rate constants with high accuracy at any value of the barrier height. For high barriers, our predictions approach (but are more accurate than) those of the classic approximate analysis of Kramers. For very low barriers (e.g., 1.6kBT), internal nonequilibrium effects neglected by Kramers are found by our theory to account for approximately 33% of the rate constant. textcopyright 1978 American Institute of Physics. |
Initial Condition Effects for Diffusive Barrier Crossing Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 69 (12), p. 5261-5266, 1978, (cited By 27). @article{Northrup19785261, title = {Initial Condition Effects for Diffusive Barrier Crossing}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.436579}, year = {1978}, date = {1978-01-01}, journal = {The Journal of Chemical Physics}, volume = {69}, number = {12}, pages = {5261-5266}, abstract = {A formulation and analysis of transient initial condition effects on reaction is given for the diffusive limit of barrier crossing between two stable chemical states. We focus on the case where the system is initially prepared in the high energy intermediate barrier region located between the stable states. It is shown how branching fluxes into and branching probabilities for stable states can be both calculated for and determined from analysis of stable state population dynamics. textcopyright 1978 American Institute of Physics.}, note = {cited By 27}, keywords = {}, pubstate = {published}, tppubtype = {article} } A formulation and analysis of transient initial condition effects on reaction is given for the diffusive limit of barrier crossing between two stable chemical states. We focus on the case where the system is initially prepared in the high energy intermediate barrier region located between the stable states. It is shown how branching fluxes into and branching probabilities for stable states can be both calculated for and determined from analysis of stable state population dynamics. textcopyright 1978 American Institute of Physics. |
Coupling of Translational and Reactive Dynamics for a Fokker-Planck Model Article de journal S H Northrup; J T Hynes The Journal of Chemical Physics, 68 (7), p. 3203-3216, 1978, (cited By 48). @article{Northrup19783203, title = {Coupling of Translational and Reactive Dynamics for a Fokker-Planck Model}, author = {S H Northrup and J T Hynes}, doi = {10.1063/1.436121}, year = {1978}, date = {1978-01-01}, journal = {The Journal of Chemical Physics}, volume = {68}, number = {7}, pages = {3203-3216}, abstract = {The coupling of translational and reactive dynamics is investigated for a Fokker-Planck description of relative particle motion in a solvent. A division into inner and outer relative coordinate spatial regions separated by a boundary layer is made. The inner region is characterized by a deep potential well associated with bound, or reacted, particles and a potential barrier. The outer zone is characterized by less rapidly varying forces which include solvent structural effects. With this division, a Fokker-Planck source equation for unreacted particles is derived. The source in this equation incorporates the complete inner region dynamics involving both reactive and nonreactive trajectories. This equation is then reduced via projection operator techniques to a spatial Smoluchowski source equation for unreacted particles in the outer region for the case of slow reaction. Validity conditions involving velocity relaxation are given. The sources here include both inner region short range repulsive effects and a reversible chemical reaction. The outer Smoluchowski description includes caging effects. The equivalent boundary condition formulation is given; thus, the radiative boundary condition relating diffusive and reactive fluxes is derived. New expressions for the reaction rate constants are found and examined in terms of more fundamental rate kernels and Fokker-Planck barrier crossing dynamics. The rate constants are evaluated for a Kramers-type treatment of the inner region. These rate constants include effects of velocity nonequilibrium. They reduce to transition state results under intermediate inner region friction conditions. textcopyright 1978 American Institute of Physics.}, note = {cited By 48}, keywords = {}, pubstate = {published}, tppubtype = {article} } The coupling of translational and reactive dynamics is investigated for a Fokker-Planck description of relative particle motion in a solvent. A division into inner and outer relative coordinate spatial regions separated by a boundary layer is made. The inner region is characterized by a deep potential well associated with bound, or reacted, particles and a potential barrier. The outer zone is characterized by less rapidly varying forces which include solvent structural effects. With this division, a Fokker-Planck source equation for unreacted particles is derived. The source in this equation incorporates the complete inner region dynamics involving both reactive and nonreactive trajectories. This equation is then reduced via projection operator techniques to a spatial Smoluchowski source equation for unreacted particles in the outer region for the case of slow reaction. Validity conditions involving velocity relaxation are given. The sources here include both inner region short range repulsive effects and a reversible chemical reaction. The outer Smoluchowski description includes caging effects. The equivalent boundary condition formulation is given; thus, the radiative boundary condition relating diffusive and reactive fluxes is derived. New expressions for the reaction rate constants are found and examined in terms of more fundamental rate kernels and Fokker-Planck barrier crossing dynamics. The rate constants are evaluated for a Kramers-type treatment of the inner region. These rate constants include effects of velocity nonequilibrium. They reduce to transition state results under intermediate inner region friction conditions. textcopyright 1978 American Institute of Physics. |
Molecular Rotation and Reorientation: Microscopic and Hydrodynamic Contributions Article de journal J T Hynes; R Kapral; M Weinberg The Journal of Chemical Physics, 69 (6), p. 2725-2733, 1978, (cited By 115). @article{Hynes19782725, title = {Molecular Rotation and Reorientation: Microscopic and Hydrodynamic Contributions}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1063/1.436868}, year = {1978}, date = {1978-01-01}, journal = {The Journal of Chemical Physics}, volume = {69}, number = {6}, pages = {2725-2733}, abstract = {The relative roles of microscopic and hydrodynamic contributions to molecular rotation and reorientation are examined within the framework of the microscopic boundary layer theory recently proposed by the authors. The theory is applied to rough spheres, for which computer simulation data are available, and to experimental results on spherical top molecules. Attention is focused on rotational diffusion constants, the kappa parameter introduced by Kivelson et al., and orientational relaxation times. It is shown that, while collective effects are present and often nonnegligible, the motion of small molecules is dominated by its microscopic aspects. Experimental trends which can incorrectly suggest dominance by hydrodynamic contributions are discussed in some detail. Finally, the transition to the regime where collective effects are dominant is considered. textcopyright 1978 American Institute of Physics.}, note = {cited By 115}, keywords = {}, pubstate = {published}, tppubtype = {article} } The relative roles of microscopic and hydrodynamic contributions to molecular rotation and reorientation are examined within the framework of the microscopic boundary layer theory recently proposed by the authors. The theory is applied to rough spheres, for which computer simulation data are available, and to experimental results on spherical top molecules. Attention is focused on rotational diffusion constants, the kappa parameter introduced by Kivelson et al., and orientational relaxation times. It is shown that, while collective effects are present and often nonnegligible, the motion of small molecules is dominated by its microscopic aspects. Experimental trends which can incorrectly suggest dominance by hydrodynamic contributions are discussed in some detail. Finally, the transition to the regime where collective effects are dominant is considered. textcopyright 1978 American Institute of Physics. |
1977 |
Slip Boundary Condition and Rough Sphere Angular Velocity Correlations Article de journal J T Hynes; R Kapral; M Weinberg Chemical Physics Letters, 47 (3), p. 575-577, 1977, (cited By 22). @article{Hynes1977575, title = {Slip Boundary Condition and Rough Sphere Angular Velocity Correlations}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0009-2614(77)85044-6}, year = {1977}, date = {1977-01-01}, journal = {Chemical Physics Letters}, volume = {47}, number = {3}, pages = {575-577}, abstract = {Angular velocity correlations for rough spheres are examined via a slip boundary condition. This condition approximately accounts for microscopic boundary layer effects and exposes both microscopic and collective decay effects. The results compare well with molecular dynamics calculations. textcopyright 1977.}, note = {cited By 22}, keywords = {}, pubstate = {published}, tppubtype = {article} } Angular velocity correlations for rough spheres are examined via a slip boundary condition. This condition approximately accounts for microscopic boundary layer effects and exposes both microscopic and collective decay effects. The results compare well with molecular dynamics calculations. textcopyright 1977. |
Slip Boundary Condition for Rough Sphere Rotation Article de journal J T Hynes; R Kapral; M Weinberg Chemical Physics Letters, 46 (3), p. 463-466, 1977, (cited By 46). @article{Hynes1977463, title = {Slip Boundary Condition for Rough Sphere Rotation}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0009-2614(77)80629-5}, year = {1977}, date = {1977-01-01}, journal = {Chemical Physics Letters}, volume = {46}, number = {3}, pages = {463-466}, abstract = {Microscopic boundary layer effects for rough sphere rotation are considered via a slip boundary condition. Predictions for diffusion constants are compared with molecular dynamics results. The slip coefficient is discussed. textcopyright 1977.}, note = {cited By 46}, keywords = {}, pubstate = {published}, tppubtype = {article} } Microscopic boundary layer effects for rough sphere rotation are considered via a slip boundary condition. Predictions for diffusion constants are compared with molecular dynamics results. The slip coefficient is discussed. textcopyright 1977. |
Particle Rotation and Translation in a Fluid with Spin Article de journal J T Hynes; R Kapral; M Weinberg Physica A: Statistical Mechanics and its Applications, 87 (3), p. 427-452, 1977, (cited By 26). @article{Hynes1977427, title = {Particle Rotation and Translation in a Fluid with Spin}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0378-4371(77)90044-9}, year = {1977}, date = {1977-01-01}, journal = {Physica A: Statistical Mechanics and its Applications}, volume = {87}, number = {3}, pages = {427-452}, abstract = {The effects of fluid spin (internal angular momentum of the fluid molecules) are examined for test particle rotation and translation. Two mechanisms of spin change, namely coupling to linear velocity and spin diffusion, are included in the full hydrodynamic description. The associated general boundary conditions are determined as linear constitutive relations on the test particle surface. Numerical calculations of rotational and translational friction are presented as functions of frequency, boundary conditions and fluid density. In addition, the deGroot-Mazur approximation which neglects spin diffusion is examined. The relevance of these results for time correlation function calculations is discussed. textcopyright 1977.}, note = {cited By 26}, keywords = {}, pubstate = {published}, tppubtype = {article} } The effects of fluid spin (internal angular momentum of the fluid molecules) are examined for test particle rotation and translation. Two mechanisms of spin change, namely coupling to linear velocity and spin diffusion, are included in the full hydrodynamic description. The associated general boundary conditions are determined as linear constitutive relations on the test particle surface. Numerical calculations of rotational and translational friction are presented as functions of frequency, boundary conditions and fluid density. In addition, the deGroot-Mazur approximation which neglects spin diffusion is examined. The relevance of these results for time correlation function calculations is discussed. textcopyright 1977. |
Microscopic Boundary Layer Effects and Rough Sphere Rotation Article de journal J T Hynes; R Kapral; M Weinberg The Journal of Chemical Physics, 67 (7), p. 3256-3267, 1977, (cited By 57). @article{Hynes19773256, title = {Microscopic Boundary Layer Effects and Rough Sphere Rotation}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1063/1.435242}, year = {1977}, date = {1977-01-01}, journal = {The Journal of Chemical Physics}, volume = {67}, number = {7}, pages = {3256-3267}, abstract = {A calculation of the rough sphere angular velocity correlation function is presented which takes into account the presence of both the microscopic boundary layer and outer hydrodynamic regions around the test particle. The boundary layer region is approximately accounted for by the slip boundary condition while generalized hydrodynamic equations (frequency dependent transport coefficients plus fluid spin variables) are used to describe the outer region. The approximate calculation of the slip coefficient and the use of the slip coefficient to account for processes occurring in the boundary layer are discussed in the context of kinetic theory results. Since a description of both regions is incorporated, the present theory contains both microscopic and collective effects. The structure of the result is compared in some detail to a recent renormalized kinetic theory calculation on the same system and various levels of approximation are examined. The results are in good agreement with the molecular dynamics calculations. Copyright textcopyright 1977 American Institute of Physics.}, note = {cited By 57}, keywords = {}, pubstate = {published}, tppubtype = {article} } A calculation of the rough sphere angular velocity correlation function is presented which takes into account the presence of both the microscopic boundary layer and outer hydrodynamic regions around the test particle. The boundary layer region is approximately accounted for by the slip boundary condition while generalized hydrodynamic equations (frequency dependent transport coefficients plus fluid spin variables) are used to describe the outer region. The approximate calculation of the slip coefficient and the use of the slip coefficient to account for processes occurring in the boundary layer are discussed in the context of kinetic theory results. Since a description of both regions is incorporated, the present theory contains both microscopic and collective effects. The structure of the result is compared in some detail to a recent renormalized kinetic theory calculation on the same system and various levels of approximation are examined. The results are in good agreement with the molecular dynamics calculations. Copyright textcopyright 1977 American Institute of Physics. |
1976 |
Rotational Relaxation for a Rough Particle Model Article de journal J E Clauter; J T Hynes Chemical Physics Letters, 38 (2), p. 248-252, 1976, (cited By 8). @article{Clauter1976248, title = {Rotational Relaxation for a Rough Particle Model}, author = {J E Clauter and J T Hynes}, doi = {10.1016/0009-2614(76)85147-0}, year = {1976}, date = {1976-01-01}, journal = {Chemical Physics Letters}, volume = {38}, number = {2}, pages = {248-252}, abstract = {Angular momentum and rotational kinetic energy relaxation for a simple model due to Widom is studied. Averages and correlation functions decay strictly exponentially, while distributions can exhibit two peak structures absent in approximate treatments but observed experimentally. textcopyright 1976.}, note = {cited By 8}, keywords = {}, pubstate = {published}, tppubtype = {article} } Angular momentum and rotational kinetic energy relaxation for a simple model due to Widom is studied. Averages and correlation functions decay strictly exponentially, while distributions can exhibit two peak structures absent in approximate treatments but observed experimentally. textcopyright 1976. |
On Exponential Time Decay in Relaxation Article de journal R I Cukier; J T Hynes The Journal of Chemical Physics, 64 (6), p. 2674-2683, 1976, (cited By 17). @article{Cukier19762674, title = {On Exponential Time Decay in Relaxation}, author = {R I Cukier and J T Hynes}, doi = {10.1063/1.432521}, year = {1976}, date = {1976-01-01}, journal = {The Journal of Chemical Physics}, volume = {64}, number = {6}, pages = {2674-2683}, abstract = {A new mechanism for approximate exponential relaxation is discussed which is significantly less restrictive than the two commonly accepted origins of exponential decay. In this mechanism, the decay rate of a time correlation function or nonequilibrium average is approximated by its exact initial value. A rationale for this approximation is discussed and related to suppression of nonlinear effects in the mode coupling formulation of relaxation. The accuracy of the approximation is demonstrated by comparison with known results for several examples of relaxation. This accuracy is maintained both where standard arguments would imply marked nonexponential behavior and where standard approximations are very poor. Copyright textcopyright 1976 American Institute of Physics.}, note = {cited By 17}, keywords = {}, pubstate = {published}, tppubtype = {article} } A new mechanism for approximate exponential relaxation is discussed which is significantly less restrictive than the two commonly accepted origins of exponential decay. In this mechanism, the decay rate of a time correlation function or nonequilibrium average is approximated by its exact initial value. A rationale for this approximation is discussed and related to suppression of nonlinear effects in the mode coupling formulation of relaxation. The accuracy of the approximation is demonstrated by comparison with known results for several examples of relaxation. This accuracy is maintained both where standard arguments would imply marked nonexponential behavior and where standard approximations are very poor. Copyright textcopyright 1976 American Institute of Physics. |
1975 |
Nonlinear Momentum Relaxation of an Impurity in a Harmonic Chain Article de journal J T Hynes; R Kapral; M Weinberg Journal of Statistical Physics, 13 (5), p. 427-449, 1975, (cited By 4). @article{Hynes1975427, title = {Nonlinear Momentum Relaxation of an Impurity in a Harmonic Chain}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1007/BF01013118}, year = {1975}, date = {1975-01-01}, journal = {Journal of Statistical Physics}, volume = {13}, number = {5}, pages = {427-449}, abstract = {A microscopic derivation of the generalized Langevin equation for arbitrary powers of the momentum of an impurity in a harmonic chain is presented. As a direct consequence of the Gaussian character of the conditional momentum distribution function, nonlinear momentum coupling effects are absent for this system and the Langevin equation takes on a particularly simple form. The kernels which characterize the decay of higher powers of the impurity momentum depend on the ratio of the masses of the impurity and bath particles, in contrast to the situation for the momentum Langevin equation for this system. The simplicity of the harmonic chain dynamics is exploited in order to investigate several features of the relaxation, such as the factorization approximation for time-dependent correlation functions and the decay of the kinetic energy autocorrelation function. textcopyright 1975 Plenum Publishing Corporation.}, note = {cited By 4}, keywords = {}, pubstate = {published}, tppubtype = {article} } A microscopic derivation of the generalized Langevin equation for arbitrary powers of the momentum of an impurity in a harmonic chain is presented. As a direct consequence of the Gaussian character of the conditional momentum distribution function, nonlinear momentum coupling effects are absent for this system and the Langevin equation takes on a particularly simple form. The kernels which characterize the decay of higher powers of the impurity momentum depend on the ratio of the masses of the impurity and bath particles, in contrast to the situation for the momentum Langevin equation for this system. The simplicity of the harmonic chain dynamics is exploited in order to investigate several features of the relaxation, such as the factorization approximation for time-dependent correlation functions and the decay of the kinetic energy autocorrelation function. textcopyright 1975 Plenum Publishing Corporation. |
Microscopic Theory of Brownian Motion. II. Nonlinear Langevin Equations Article de journal J T Hynes; R Kapral; M Weinberg Physica A: Statistical Mechanics and its Applications, 81 (4), p. 485-508, 1975, (cited By 15). @article{Hynes1975485, title = {Microscopic Theory of Brownian Motion. II. Nonlinear Langevin Equations}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0378-4371(75)90071-0}, year = {1975}, date = {1975-01-01}, journal = {Physica A: Statistical Mechanics and its Applications}, volume = {81}, number = {4}, pages = {485-508}, abstract = {In this article nonlinear Langevin equations for a brownian (B) particle are derived and analyzed. Attention is focussed on the role of nonlinear B particle momentum (P) modes (powers of P). The multimode Mori formalism is used to derive equations of motion for P(t) for different numbers n of modes included in the description. The well-known linear equation of Mori corresponds to the case n = 1. Friction kernels and random forces in these equations exhibit slow decay and mass ratio ($\lambda$) expansion anomalies due to mode coupling. The nonlinear Langevin equation obtained for a complete mode set (n = $infty$) is free of these difficulties and is used to examine the first correction [O($\lambda$4)] to standard O($\lambda$2) results. Although no closed set of nonlinear Langevin equations exists at order $\lambda$4, a truncated set extends standard momentum correlation function predictions. textcopyright 1975.}, note = {cited By 15}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this article nonlinear Langevin equations for a brownian (B) particle are derived and analyzed. Attention is focussed on the role of nonlinear B particle momentum (P) modes (powers of P). The multimode Mori formalism is used to derive equations of motion for P(t) for different numbers n of modes included in the description. The well-known linear equation of Mori corresponds to the case n = 1. Friction kernels and random forces in these equations exhibit slow decay and mass ratio ($łambda$) expansion anomalies due to mode coupling. The nonlinear Langevin equation obtained for a complete mode set (n = $infty$) is free of these difficulties and is used to examine the first correction [O($łambda$4)] to standard O($łambda$2) results. Although no closed set of nonlinear Langevin equations exists at order $łambda$4, a truncated set extends standard momentum correlation function predictions. textcopyright 1975. |
Microscopic Theory of Brownian Motion: Mori Friction Kernel and Langevin-Equation Derivation Article de journal J T Hynes; R Kapral; M Weinberg Physica A: Statistical Mechanics and its Applications, 80 (2), p. 105-127, 1975, (cited By 23). @article{Hynes1975105, title = {Microscopic Theory of Brownian Motion: Mori Friction Kernel and Langevin-Equation Derivation}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0378-4371(75)90162-4}, year = {1975}, date = {1975-01-01}, journal = {Physica A: Statistical Mechanics and its Applications}, volume = {80}, number = {2}, pages = {105-127}, abstract = {A derivation of the phenomenological Langevin equation for the momentum of a brownian particle from the generalized Langevin equation of Mori is presented. This derivation requires a detailed examination of the Mori friction kernel (or memory function). It is demonstrated, on the basis of prior work of Mazur and Oppenheim, that the Mori kernel does not admit of a well behaved expansion in the ratio of bath- and brownian-particle masses. In addition, the Mori kernel is found to decay on the slow time scale of the brownian-particle momentum. Both features, which contradict standard assumption, are traced to the influence of coupling to nonlinear powers of the momentum and preclude a Langevin-equation derivation solely on the basis of time-scale separation arguments. The Langevin-equation is recovered, however, when the small magnitude of slowly decaying contributions is taken into account. textcopyright 1975.}, note = {cited By 23}, keywords = {}, pubstate = {published}, tppubtype = {article} } A derivation of the phenomenological Langevin equation for the momentum of a brownian particle from the generalized Langevin equation of Mori is presented. This derivation requires a detailed examination of the Mori friction kernel (or memory function). It is demonstrated, on the basis of prior work of Mazur and Oppenheim, that the Mori kernel does not admit of a well behaved expansion in the ratio of bath- and brownian-particle masses. In addition, the Mori kernel is found to decay on the slow time scale of the brownian-particle momentum. Both features, which contradict standard assumption, are traced to the influence of coupling to nonlinear powers of the momentum and preclude a Langevin-equation derivation solely on the basis of time-scale separation arguments. The Langevin-equation is recovered, however, when the small magnitude of slowly decaying contributions is taken into account. textcopyright 1975. |
Microscopic Theory of Brownian Motion. III. The Nonlinear Fokker-Planck Equation Article de journal J T Hynes; R Kapral; M Weinberg Physica A: Statistical Mechanics and its Applications, 81 (4), p. 509-521, 1975, (cited By 8). @article{Hynes1975509, title = {Microscopic Theory of Brownian Motion. III. The Nonlinear Fokker-Planck Equation}, author = {J T Hynes and R Kapral and M Weinberg}, doi = {10.1016/0378-4371(75)90072-2}, year = {1975}, date = {1975-01-01}, journal = {Physica A: Statistical Mechanics and its Applications}, volume = {81}, number = {4}, pages = {509-521}, abstract = {The nonlinear Fokker-Planck equation for the momentum distribution of a brownian particle of mass M in a bath of particles of mass m is derived. The contribution to this equation arising from initial deviation from bath equilibrium is analysed. This contribution is free of slow M-dependent decays and with certain restrictions leads to an effective shift in the initial value of the B particle momentum. The nonlinear Fokker-Planck equation for an initial bath equilibrium state is analyzed in terms of its predictions for momentum relaxation and mode coupling effects. It is found that in addition to nonlinear renormalization of the type previously found for the momentum correlation function, mode coupling leads to long-lived memory of the initial momentum state. textcopyright 1975.}, note = {cited By 8}, keywords = {}, pubstate = {published}, tppubtype = {article} } The nonlinear Fokker-Planck equation for the momentum distribution of a brownian particle of mass M in a bath of particles of mass m is derived. The contribution to this equation arising from initial deviation from bath equilibrium is analysed. This contribution is free of slow M-dependent decays and with certain restrictions leads to an effective shift in the initial value of the B particle momentum. The nonlinear Fokker-Planck equation for an initial bath equilibrium state is analyzed in terms of its predictions for momentum relaxation and mode coupling effects. It is found that in addition to nonlinear renormalization of the type previously found for the momentum correlation function, mode coupling leads to long-lived memory of the initial momentum state. textcopyright 1975. |
1974 |
Nonlinear Fluctuations in Master Equation Systems. I. Velocity Correlation Function for the Rayleigh Model Article de journal J T Hynes The Journal of Chemical Physics, 62 (8), p. 2972-2981, 1974, (cited By 17). @article{Hynes19742972, title = {Nonlinear Fluctuations in Master Equation Systems. I. Velocity Correlation Function for the Rayleigh Model}, author = {J T Hynes}, year = {1974}, date = {1974-01-01}, journal = {The Journal of Chemical Physics}, volume = {62}, number = {8}, pages = {2972-2981}, abstract = {The influence of nonlinear velocity fluctuations on the velocity correlation function $Pi$(t) is studied for the Rayleigh model of a massive particle in an ideal gas as an example of a master equation system. It is shown that the Mori kernel K(t), which determines the decay of $Pi$(t), has a slow mass-dependent decay on the time scale of the decay of $Pi$(t) and has no well-behaved expansion in the mass ratio. Both features are contrary to standard assumption. The origins of the slow decay are traced to nonlinear fluctuations and the relationship to previous work on requisite conditions for exact exponential decay is discussed. The slow decay of $Pi$(t) is shown to lead to divergent "Burnett" coefficients in macroscopic friction laws and the resolution of this difficulty is discussed. The relationship of the microscopic "bare" friction constant to the macroscopic friction constant is considered. Explicit expressions for $Pi$(t) and K(t) for small mass ratio are obtained by mode-mode coupling analysis and perturbation methods. The influence of nonlinear fluctuation effects is found to be numerically negligible despite their long lifetime. The remaining deviation from standard Brownian motion results is examined numerically. The validity of some standard assumptions in mode-mode coupling theory is also examined. Copyright textcopyright 1975 American Institute of Physics.}, note = {cited By 17}, keywords = {}, pubstate = {published}, tppubtype = {article} } The influence of nonlinear velocity fluctuations on the velocity correlation function $Pi$(t) is studied for the Rayleigh model of a massive particle in an ideal gas as an example of a master equation system. It is shown that the Mori kernel K(t), which determines the decay of $Pi$(t), has a slow mass-dependent decay on the time scale of the decay of $Pi$(t) and has no well-behaved expansion in the mass ratio. Both features are contrary to standard assumption. The origins of the slow decay are traced to nonlinear fluctuations and the relationship to previous work on requisite conditions for exact exponential decay is discussed. The slow decay of $Pi$(t) is shown to lead to divergent "Burnett" coefficients in macroscopic friction laws and the resolution of this difficulty is discussed. The relationship of the microscopic "bare" friction constant to the macroscopic friction constant is considered. Explicit expressions for $Pi$(t) and K(t) for small mass ratio are obtained by mode-mode coupling analysis and perturbation methods. The influence of nonlinear fluctuation effects is found to be numerically negligible despite their long lifetime. The remaining deviation from standard Brownian motion results is examined numerically. The validity of some standard assumptions in mode-mode coupling theory is also examined. Copyright textcopyright 1975 American Institute of Physics. |
Initial Condition Effects for a Brownian Particle in a Harmonic Chain Article de journal J T Hynes Journal of Statistical Physics, 11 (3), p. 257-275, 1974, (cited By 11). @article{Hynes1974257, title = {Initial Condition Effects for a Brownian Particle in a Harmonic Chain}, author = {J T Hynes}, doi = {10.1007/BF01010220}, year = {1974}, date = {1974-01-01}, journal = {Journal of Statistical Physics}, volume = {11}, number = {3}, pages = {257-275}, abstract = {The influence of initial deviations from bath equilibrium on the motion of a Brownian particle in a harmonic chain is investigated by exact calculation. These initial condition effects, which are excluded by convention in standard projection operator treatments of relaxation processes, are found to be relatively long-lived, contrary to usual assumption. For weak, localized initial deviations from bath equilibrium these effects on the motion are small in magnitude and may be accounted for by a modified initial condition on the particle velocity. For initial deviations involving many bath particles these effects are more substantial and retention of their time dependence in the particle equation of motion is generally required. textcopyright 1974 Plenum Publishing Corporation.}, note = {cited By 11}, keywords = {}, pubstate = {published}, tppubtype = {article} } The influence of initial deviations from bath equilibrium on the motion of a Brownian particle in a harmonic chain is investigated by exact calculation. These initial condition effects, which are excluded by convention in standard projection operator treatments of relaxation processes, are found to be relatively long-lived, contrary to usual assumption. For weak, localized initial deviations from bath equilibrium these effects on the motion are small in magnitude and may be accounted for by a modified initial condition on the particle velocity. For initial deviations involving many bath particles these effects are more substantial and retention of their time dependence in the particle equation of motion is generally required. textcopyright 1974 Plenum Publishing Corporation. |